[QUOTE=Dinsdale]
If A=440 Hz, why call them all A’s then, no matter where they appear on sheet music? Isn’t a tone value pretty universal…?
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It is now. We can ask this question in hindsight and say, gee, why wasn’t this all standardized a long time ago?
Time for the wayback machine and to mention some things from the history of music that may have had a contributing effect. None of these are directly responsible for transposing instruments, but it’ll give you an idea what musical instrument makers were thinking.
The idea that 440 Hz = concert A is relatively recent. It was established as international standard for Western music in 1939. Prior to that, A was 435 Hz. Prior to that, A was anywhere from 400 Hz to 450 Hz based on the tuning fork that the performance hall happened to have(Cite.) To make matters worse, because there was no electronic sound reproduction to enhance the sound of an instrument, one of the easiest ways to make an instrument sound brighter and livelier — and thus louder — was to raise its pitch slightly.
When your pipe organ went out of tune, and the top of the pipe was cracked or frayed, what did you do? Slice a bit off the top of all the pipes, that’s what. This would serve to raise the instrument’s pitch each time you “tuned” it.
By the time anybody had measuring devices fine enough for that kind of accuracy, or was committed to deciding on a standard, we already had dozens of instruments being made to very specific pitch ranges.
Now the pitch of a stringed instrument, like cello or guitar, depends on the length of the string and can be tuned by twisting the key on the instrument’s neck. Not so with brass: there the pitch is set by the interior volume of the instrument. It can be fine-tuned by adjusting the mouthpiece, lengthening or shortening the interior of the tube slightly, but it cannot be easily tuned up or down great distances. If you played trumpet, and went to a different city where you had a different pitch range, you’d need a different instrument that could be more finely tuned to that range.
A moment’s thought will serve to show why you can’t make a miniature tuba: by shrinking the interior volume of the instrument’s tubing, you raise the pitch.
So there are half a dozen different kinds of saxophones, not because we like the painful redundancies and mental gymnastics of transposition, but because you can’t make a tenor sax the size of a clarinet by using brass and leather. The physics of sound is in the way.
Also, back in the day, you couldn’t have a flat on every note. The flat symbol is shaped like a B, because that used to be the only note you could make flat. The twelve-tone chromatic scale wasn’t popular at the time because it produced some dissonant intervals (such as a diminished fifth) that people thought was diabolus in musica (“the devil in music”) and the interval was avoided in composition. Though we’re accustomed to instruments today that have the full range of twelve-tone polyphony, producing every note (C C# D D# E F F# G G# A A# B) it wasn’t always so.
Now throw in even temperament. The way instruments are tuned today, C# and Db are equivalent —enharmonic, we’d say. That wasn’t always so either. Once upon a time, they were unique notes — and that meant if you wanted to play in A, it had an entirely unique tuning.
That’s why the instruments have different sounds: the limitations of sound and size, and a long-standing tradition of non-standardized concert pitch. But why do we call the notes by different names when clearly we mean a certain arbitrary frequency?
Saxophones are all fingered more or less the same way, and read on the same lines of sheet music. This reduces the burden on the bag of wind who’s blowing the horn, and increases the burden on the bag of wind who wrote the music. 
I presume the popularity of transposing instruments came from the painful reality that the average person wasn’t taking music classes daily in school, and multi-instrument virtuosos were hard to come by. It was probably deemed simpler to have one fingering and one staff notation for all saxophones and make the composer — who was usually wealthier and better-educated — do the heavy lifting.
Nowadays, where you can find decent musicians in any elementary school, and where pitches have been standardized, it makes much less sense.
Is this a 100% accurate reason why we have transposing instruments? I doubt it; I’m no music scholar. I fully expect someone to come along with corrections or refinements. It might give you the background to understand how we got to this point, though.