I’m not quite sure I see how these things really gel together. You either want it short, sweet, and to the point, or you want the details. You can’t really have both, it’s just not the way people work.
Unless you’re on the stand in a court of law, this just sounds like casual conversation to me.
Otherwise, replying “Yes, I am vacationing in Alaska at month’s end.” seems stilted, void of personality, and doesn’t really invite conversation.
I’d be more apt to say something like, “Yep! I’m going at the end of the month!”
It’s just how people talk.
This is how I feel about it. Saying “He is.” is exactly the same as saying “Yes, he is.” With the affirmative tone, the yes is usually pretty clearly implied. Obviously, it’s a little silly for some questions because the clarification isn’t necessary, but it does come off less curt.
For other questions like “Did you go to the store?” Sure, “Yes” is fine, and say “I did” doesn’t add anything. But, asking “Didn’t you go to the store?” a simple “Yes” can be ambiguous because though, as someone mentioned, because of the negative you should technically say no, but customarily one will say yes, so saying “I did” clearly answers a yes or no and succinctly answers what is technically a yes or no question where yes or no can’t.
But really, if you want to get into it, though they’re technically the same question, just one is asking in the negative, the implications behind the questions are different. The first one is simply asking because they don’t know where usually asking “Didn’t you…?” carries the implication that they believe that you did or that you should have and wanted confirmation. In the same way, “Yes” is just an answer but “I am” or “I did” will often have a bit more subtext to it.
And I think that’s a lot of why you hear it on the radio. Of course, a good interviewer shouldn’t just ask a bunch of yes or no questions, but a good interviewee should want to make their answers more interesting. It’s not nearly as interesting to just hear yes and no over and over again when one can use variations that add that subtext or add some amount of enthusiasm or fuzziness or whatever to their answer.
There are languages (Welsh, for example, as cited in a link upthread) that do not have a proper word for yes or no in the sense that you want. Those languages answer by the method you object to. Although English does have yes and no for the purpose, nevertheless, the method you object to is still also correct English. Your peeve peeves me. Suffer.
I agree
If I may…I’ve noticed that many people are answering their cell phones with “hey” instead of Hello, Hi, etc.
Have you?
Is it possible that people who do this also avoid saying “black” or “white”?
Awww… don’t be that way. 
I admitted it was nit-picky to the max, and anyway you told me something really interesting about Welsh. It’s interesting how the vocabulary we have at our disposal shapes the thoughts before they become words.
I really like Cheshire cheese. When toasted, it turns into a magical, delicious substance with a crispy, yummy nuttiness. I understand it’s one of the oldest cheeses in the world and that when the Romans came to Britain, they used to toast it on the the points of their swords in front of the campfire.
I know what you’re talking about, ThelmaLou. Just the other day I heard myself answering questions in that nonsensically emphatic way for the first time ever. It disturbed me, because it’s not natural to my style of speaking. Something is in the air.
Meh, I just like people to pick one.
“Are you going to the store?”
“Yeah, no.”
??
Affirmative.
I’d find the kind of responses mentioned in the OP unusual, but they convey the desired meaning, so it’s ok.
What drives me up a wall and down the other is people who answer an “A or B” question with “yes”. Yes what? Yes A, yes B, or yes you may give me a swift kick on the behind to help me wake up?
Maybe the OP’s irritators know too many of the ones who irritate me.
I prefer the form of answer the OP is describing - it just seems more precise and unambiguous - especially in cases where the question may contain a negative term (“Didn’t you say you had a table saw in your garage?”), or for long, rambling questions where the part you’re responding to is right at the start - and listeners (indeed even the questioner) might have lost track of what was the actual question.
Presidential campaign year.
I find a lot of people are especially averse to the word ‘no’. I think they are so averse to delivering bad news so they avoid the word, even when the context might not mean a bad thing.
Thank you for that. 
I completely agree with this! And what makes it worse is when they say it with a smug smile, like they think they’re being witty or cute, or like they’re the first person to ever think this up.
I think this is absolutely true, too. If you say “no,” even if no is the true answer, then you’re a “negative person.” Puh-leese. Sometimes no or even HELL NO! is the right anwer: “Do you want to go with me to the dogfight tonight?” “I don’t,” sounds wimpy and regretful, when the proper answer is “Fuck no! And don’t ever ask me again!”
Speaking of being negative, many years ago (mid-1960’s), I worked at a telephone answering service. (We sat at a switchboard and answered the phone and took messages for businesses after hours or when they were out.) We operators were forbidden to answer a question with the exact phrase, “I don’t know.” We couldn’t say it to callers TO the business or to the businesses when they called in to pick up their messages. We had a whole raft of permissible phrases to use instead: “He didn’t give me that information,” “I’ll find out for you,” “I’ll ask Mr. Jones to call you with that information.” I guess my bosses felt that to say “I don’t know” made the answering service look like we weren’t on the ball. Maybe they were right, as when one says “I don’t know,” someone can reply, “Well. why DON’T you know?” or “Well, who DOES?” or “What DO you know??” That job could be stressful…
Well, don’t take it too hard, your peeve doesn’t peeve me that much.
Incidentally, I’m named for the Cheshire Cat from Alice in Wonderland, not for the cheese. I never knew there was a Cheshire cheese. I’ll have to look for it and try it like you suggest.
This one peeves me too, but from the opposite direction. The people asking the question start out with “A” and then pause, so I answer with “yes or no”, but then as I am answering, they add the “B” option, and then get upset that my answer was “yes or no” to the first, rather than the “A or B” that they wanted. Look, people, if you’re going to phrase your question as “A or B”, don’t pause between the options, and then complain when people answer the first half as “yes or no”. If you are getting a lot of those types of responses, you might want to examine how you are asking the question. It may well be your fault that you get so many of the type of response you are objecting to.
Some people will ask the question thusly:
Q. Are you going to Alaska on your vacation next year, or not?
Q. Are you going to eat the last piece of pizza or not?
Q. Is that new TV show horrible or what?
In such cases, it’s a lot clearer to answer something like “I am” or “It is” than just “Yes” or “No.” And if enough people ask you questions like that, you get in the habit of giving non-yes/no answers even when it would be perfectly clear to do so.
Yes, Irish is another of those languages. The OP should probably never go to Ireland if he/she doesn’t want to be peeved into oblivion. This form of answering a question with ‘I did’ or ‘I didn’t’ etc. made its way from Irish into Hiberno-English and is very common still today.