Using the term "alto clarinet" when referring to the basset horn is insulting to basset horns, horns of any type, and (for all I know) basset hounds and Angela Bassett. Let's watch our language, shall we?
There is some evidence that Anton Stadtler used a clarinet with special keywork to low C when performing the original version of the Mozart work. But, I haven't read anything that was absolutely, 100% conclusive on the topic. Most of the speculation was based upon a fragment of the Concerto that was found separate from the accepted one, or at least not included in the version published "at the time".
In the days of the simple, six key clarinet, such an instrument (where all of the keys on the extremely long lower joint would have had to be operated by "clapper"-style levers, not interconnected in any way) would have been considered a mechanical monstrosity.
Regarding "full Boehm" clarinets, not only can you buy such instruments in Bb and A, but Selmer also produced them in Eb.
One sold on eBay a few years ago; a beautiful little instrument with silver plated keywork. From the extensive photos, it looked to be in mint condition, as you would expect an Eb clarinet to be.
I bid that sucker up pretty high, but didn't win, upon reflection that being a good thing as the sale originated in Italy, a supposed hot bed of eBay fraud.
I haven't seen a Leblanc catalog in many, many years, but I seem to recall that they offered all of their soprano clarinets with "full Boehm" keywork. I remember photographs of such instruments, including clarinets in Bb, A, C, D and Eb. But, it was a long, long time ago.
And finally, the professional Selmer bass clarinets are (in effect) offered with as close to "full Boehm" keywork as they can get. The alternate Eb, articulated G# and low Eb (for transposing A bass clarinet parts, a vital addition to any professional instrument as A bass clarinets are very thin on the ground these days) are all there and functional (and seldom if ever called "too complicated" by those who use them, unlike the soprano versions of the same thing.
All that is missing is the forked Eb/Bb mechanism. Looking at the Sax-designed LH plateau work, I can't see a way that the same facility could be offered on the bass, at least without adding another barrel and axle atop the already high stuff that's already there.
And, recalling only too well the muffled effect that the Leblanc fork Eb/Ab mechanism (operated by the right hand) had on their professional bass clarinet, I'm not so sure that I'd want to have the same "benefits" carried over to the left hand as well.
And, as an afterthought, it has always bothered me that the "Boehm" system is used to refer to the clarinets that the non-Germanic parts of the world almost universally play. While it is true that Boehm was responsible for the "regularization" of the flute, making it the vile instrument that it has become today, he didn't do squat about the clarinet.
Hyacinthe Klose (without the accents) took the Boehm system of rings used to operate connected key cups (called Brille in German, or "eyeglasses" for their resemblance to eyeglass frames) and applied them, along with many other improvements of his own devising, to straighten out all of the inconsistencies of the "simple" clarinet. As far as anyone can determine, Oswald Boehm had nothing at all to do with the whole process.
We don't call oboes or bassoons with ring keys "Boehm system oboes" or "Boehm system bassoons" (although I understand that there is such a thing in the bassoon world as well); why should we do so for clarinets?
That's enough for now - I'll save my diatribe on why alto clarinets don't need a bell for later...
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