Mozart is the greatest composer? I think not. That word is reserved for Beethoven. As a pianist, he was crap. Beethoven said he played too "choppy" and probably because of this is why Luddy stressed the legato so much. But before, he admired Mozart very much. It was probably a let down when he heard him play the piano.
Anyway, Mozart wrote a lot of crap. Beethoven did not. Mozart's philosophy on composition: he just writes without second thought. If he makes a mistake, he'll "just write another one". Beethoven was completely the opposite. Why this comparison? Because Mozart wrote many symphonies, piano pieces, and others but on a select few of them are ever heard regularly. Why is that? As I said before: he wrote a lot of crap.
Horowits, Uchida, de la Rocha, they all played Mozart better than Mozart could play Mozart. To say he was a virtuoso is to say that musicians really really sucked during the 18th century. Children usually play by strict tempo. Mozart played this way. The best interpreter of the way Mozart played, himself, is not Horowits, Uchida, or de la Rocha, but children. I may be exagerating just a little.
About his composing method: it seems very clear to me that he composed with only the range of his modern day piano in mind. Only 5 octaves so all notes would fit onto that keyboard. So what you do not get is BASS... the low frequency vibrations that "moves" more than high frequency vibrations. Beethoven knew the effect of the bass notes. Mozart did not - he kept in the middle of the piano and did not venture too far away from home key. But should you blame him for the piano technology of his day? Perhaps not. BUT! That does not excuse him for his symphonies, which were written in the same minute range of manner.
Mozart's music lacks depth. It is by chance that he was able to pluck out a few memorable tunes out of the thousands of works he wrote. His methodoly can be characterized as random where once in a while, that "nice tune" and development of that tune stick with us and gives us a sense that he was "great". Even dogs can say "mommy" if it groans long enough.
One of his popular tunes is the Ronda turkish march. I hate this. I have attempted to play it with more range and it sounds so much better the way I have re-written him. The rondo could have been further extended beyond the simple rondo format - he left many ideas un-explored in this piece. Beethoven would not have done this.
So in conclusion: Mozart wrote a lot of crap, not just for the piano but for almost all of his works, and only once in a long while did he ever pluck out memorable, yet simplistic, tunes. Am I being too harsh? Beethoven wouldn't think so.