They aren’t ideograms either; they’re logograms. Each character represents a word. Some work as pictograms; some work as ideograms. But all of them are logograms.
This is the key. People say that Chinese has tons of homonyms which is why we can’t switch to Pinyin. But that doesn’t make sense – if this were actually true, then why aren’t people bamboozled all the time when listening to spoken Chinese? Sure, people get confused once in a while, but people get confused by homonyms in English and in French (Je suis venu à sept heures vs Je suis venu à cette heure, which sound exactly the same when spoken aloud) too. Clearly Chinese people don’t spend half their lives trying to decipher what others are saying.
This line of thinking only makes marginal sense when you consider two factors:
(1) Classical Chinese cannot be written using only pinyin; and
(2) Formal modern written Chinese tends to use a large number of classical Chinese constructions.
As others have said, classical Chinese is an ossified construction. Because of all the phonetic collapses to modern Mandarin, reading classical Chinese aloud is gibberish because there are so many homonyms. Three different characters that might now all be pronounced yi were probably pronounced differently aloud say 2000 years ago, helping to maintain the difference. Classical Chinese relies heavily on one-syllable morphemes (units of meaning). By contrast, modern Mandarin relies extremely heavily on two-syllable compounds (yisheng ‘doctor’, shuxue ‘math’, gongke ‘homework’, etc.) That’s a large part of why it’s intelligible when spoken aloud and thus can be written solely using pinyin.
However, as I mentioned above, formal modern written Chinese does tend to use a rather large number of classical Chinese constructions, many of which are opaque in writing and rather like English idioms in speech (cf how you can’t get the meaning of “make up” from “make” + “up”, you have to learn it). This is where writing Mandarin with Pinyin would get confusing, because many of these constructions would become opaque and unclear. It’s sort of as if modern French or Spanish used a large number of Latin vocabulary and idioms, which you just sort of had to learn because they didn’t really conform to modern French or Spanish grammar.
I’d guess that if modern Chinese moved to being written by an alphabet, the percentage of these elements in modern formal writing would shrink, bringing it closer in line to speech.
So in a technical sense, there’s no difficulty, and Chinese is not some sort of sui generis language. On the other hand, there are tremendous cultural impediments to abandoning Chinese characters, which is why I don’t think it will happen in our lifetimes.
The way things are going, someone 100 years from now will be asking: Why did it take the rest of world so long to switch to using Chinese characters for writing? 
Because the alphabet can’t think the way the Chinese do. Its like wearing the wrong shoes to a marathon.
Ooop, I meant “phonetic alphabet languages”. I think I grabbed the phrase from the post I was responding and not realize… near zero sleep over 36 hrs…
Somehow that makes sense… 
Back in the early 1960s, my mother taught for a short time at a school at Stratford, a suburb on the east side of London about 10 km from the centre of London. There were people living there who had never been to the West End of London: a trip that would have cost just a shilling or so back then, and taken just a few minutes on the Underground. (Since I’d been born in Australia, and made the trip to England twice by the time I was a teenager, this really amazed me.)
You might be surprised how often it really does happen in conversations. I spent over 7 years in Taiwan and can tell you that people “writing” on their palms with their fingers is a very common occurrence.
Japanese and Chinese will do this, too, to aid in communication. The characters don’t correspond to exactly the same words, but many are identical or close enough.
I spent quite a bit of time in Japan before traveling to Taiwan for the first time. I worked at learning as much spoken and written Japanese as I could, and I was astounded at how much I could read in Taiwan without knowing anything other than ni hou ma in Mandarin. Street signs, food items-- many of the basics are the same. And it creates a strange situation where it’s so much easier to read than to write. I can probably read 10x the number of characters I can write. But then I almost never have occasion to write in either language.
What about things like televised speeches, where the person listening can’t ask for clarification? Are the speechwriters just extra careful to clarify in advance? Does it sometimes lead to amusing gaffes where the speaker can be interpreted as meaning something absurd?
I agree that the “homonym” thing is a bit overblown. Chinese is an aggressively disyllabic language, with the vast majority of words are created from two or more syllables. You pretty much never say a single Chinese syllable aloud on it’s own. Should you happen to have to say a single syllable word, you almost always end up tacking on some other word because it feels so damn wrong to just say one syllable. You can’t just “drink,” you need to “drink water” or “drink beer” or whatever. You pretty much never just say “water”, you need to have "hot water’ or “cold water” or something… The aversion to single syllables is so strong that sometimes you’ll just repeat a word twice rather than letting a single syllable just hang there like that.
So you aren’t really going to get xǐyījī (washing machine) mixed up with a Jīchì (chicken wing) any more than you are going to get “person” mixed up with “bumper” or “per capita” or a “watermelon” with a “waterpark”.
Damn, beaten to the di-syllabic punch by Even Sven. 
Context is pretty big. Chronos, you could try to figure out absurd characters and meanings that sound the same. Think the English equivalent of “which” and “witch”. Contextually that should be pretty clear. Chinese has a lot more words that sound the same, so it does get more complicated.
Chinese is a very logical language in terms of building blocks. A specific character is usually has a root meaning that stays pretty constant. Hand (手）would be used for “hand” “clap your hand” “hand set (mobile phone)” “glove” “hankerchief” etc. Whereas in English, “glove” is a completely unrelated sounding and meaning word to “hand”, whereas in Chinese (手套）is “hand-cover.”
In other words, two unrelated characters can be combined and the reader can guess at the meaning. Eg, if you understand character A and understand character B, you can probably guess with the combined character AB means. An english equivalent would be “air” + “port” or “sea” + “port” or “space” + “port”
Spoken and written chinese is made clearer by the process of di-syllabicization (use two syllables/2 characters instead of one). English equivalent would be to say “go out” instead of only “go”. If you were to just say “go” there might be multiple words that sound the same, whereas saying “go out” would be one or only a few combinations with that sound.
Do you have any basis for writing this?
Confucious would not recognize most of the characters because they have evolved since then, and more specifically have gone through a couple of rounds of simplification over the past 100 years. Secondly, written Chinese switched from classical to modern over the past century as well. Lu Xun maybe being the most famous example of writing in the “new style”, and written Chinese has changed much since his time.
Confucious would categorically not be able to read a modern Chinese newspaper.
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To me, this looks more like a turtle.
Like China Guy wrote, context takes care of most situations. Otherwise, yes, writers will try to avoid using some words, or will take care to provide proper context.
One common coping strategy of Japanese speakers, when palm-writing isn’t an option, is to explain the word by using more common words that use the same characters. For instance, in a recent class, I was talking about Charles Sanders Peirce and introduced his concept of icon, which has been translated as 類像. It’s pronounced ruizou but no one would ever know what I was talking about if I just dropped the word like that. So I explained it as rui like in ruiji (similar) and zou like in gazou (image).
My guess would be that that’s because した is also the past tense of する, a more commonly-used word than 下, and one for which there is no kanji in use.
Alas, I don’t think we’re any closer to answering my original question.
I cannot dispute what you say, but the claim that you can read Kanji more easily than Hira gana (which I don’t doubt) reminds me of the fact that Fibonacci brought Hindu-Arabic numerals back from his business sojourns in Arabia, people resisted using them for centuries because they were “too hard to read” compared with good old Roman numerals. My second observation was that when I visited a research institute in Japan, I noticed that a number of the notices on the bulletin board (why was I looking at things I could not make any sense of? Curiosity.) would have an occasional Kanji character that had hira gana printed above them in tiny type. I asked my host about this and he said that it was because the administration was always showing off their ability to use fancy words (really?!!) but they also wanted to make sure they were understood. The third thing I might mention is that my host gave a lecture in Japanese and invited me to come. I did out of courtesy, not understanding a thing of course. But afterwards I asked him whether he could write English or Kanji more quickly when he lectured (his English was excellent, I might mention). Oh, English for sure, could be written more quickly.
Yes, there are lots of homonyms. Of course, English lacks homonyms so we can use alphabets, right? The standard way to type Japanese is to enter the roman equivalent and choose from the computer display, in the case of homonyms, which one you mean.
I had an aunt who married a guy from Brooklyn. Now she did visit her family in Philadelphia regularly, but she once told me that in 30 years of living in Brooklyn, she had been to Manhattan just once!
I think you underestimate the number of homonyms in Japanese.
以降, 意向, 移行, 移項, 威光, 伊興, 偉効, 衣桁, 遺稿, 偉功, 遺構, 一向, 韋后, 胃腔, 維綱, 衣香, 行こう, 往こう, 逝こう, 憩う, 厳う
That’s 21 words; every one of them is read ikou. That’s one of the more extreme cases, but for words of Chinese origin (accounting for close to half the vocabulary) almost none lack homonyms. You cannot base an argument on comparisons with English.
Korean, on the other hand, is in a situation similar to Japanese, but uses an alphabet. It’s thus not completely unfathomable that Japanese would be written phonetically. However, that would mean changing writing habits and losing “backwards compatibility” with a number of texts.