> Mozart composed somewhere less than 700 works (according to wikipedia), and for your point about misappropriation to amount of a disproof, this production should account for at least of 70 % of all works during the period (else the assertion of "plenty other" still stands).
I'm refuting OP's claim that people today are generally hearing something "particularly wonderful" in Mozart's output and applying that level of extraordinary output to music from the "age of Mozart." In order to do that, all I really need to get started is a single case of a scholar tasked with cataloging all of Mozart's "particularly wonderful" output and mis-attributing the work of a "lesser" composer to Mozart. There are in fact many cases of that. So if scholars can't always tell the difference between "piece written during the time of Mozart" and bona fide "output of Mozart," it brings into question OP's initial assumption that "we"-- e.g., non-expert listeners-- are generally hearing something "particularly wonderful" in Mozart's output. It's much more likely we're hearing something "particularly 18th century"-- in terms of lightness of texture, balance of phrasing, catchy melody-and-accompaniment textures, etc.-- finding that wonderful, and ascribing that wonder to the genius of Mozart because we generally don't seek out the work of other composers from the period unless we're experts.
The point about bad musicians in bars is irrelevant. If we're to be generous, we understand when people pine for the "age of Mozart" they're speaking about traveling back in time to the late 18th-century (probably to Vienna) as a rich person, probably of nobility, and seeking out all the venues where the type of music Mozart became famous for was performed. That would be concert halls, churches, various subscription concert venues, and opera halls. The music of other composers played in those places would have had the same characteristics which "we" today find wonderful in his output. It would have also been performed quite well. If anything it would convince such a time-traveler beautiful music in that style does not require a one-in-a-civilization genius to produce.
Also-- even the narrow assertion that late 18th-century Austrian bar music is "not so different" from music today is almost certainly wrong. Just comparing bars to bars-- in nearly every facet of music I can think of-- melody, rhythm, harmony, tempo, genre, lyrical content, timbre, form, allusions to other music, spatialization, improvisation, price, accessibility-- we have vastly more variety in terms of what you might hear when you walk into a bar. And that variety ends up providing way more quality music today than was available or even conceivable to your average Austrian bargoer in the late-18th century. Just consider it-- if you got transported to the past and came back you'd say you heard some repetitive out of tune music. If one of them got transported here and back they'd spend the rest of their lives trying to explain how some guy's cheap walmart keyboard "can produce all the sounds of our modern orchestra." It's not even close.