I think it is true that Fats Waller is one of the greatest jazz composer, he has developed styles and timing that have been used lots of time after his influence. He has integrated all kinds of entertainment medium to the jazz phenomena for a long time. I think he will be remembered as one of the greats.
Fats Waller was an African-American jazz pianist, organist, composer, and entertainer. He was also one of the most beloved personalities in American music and one of jazz music’s brightest stars. I could even argue that he was the greatest jazz compose of all times. Just as he was influenced by his elders, particularly James P. Johnson, Waller had himself a considerable influence on other pianists. Most important among them are Art Tatum, the ultimate virtuoso of the instrument, and Count Basie.
Yes,there will be those who will say that Fat Waller was the best Jazz Composer of all time but others wouldn't agree. It comes down to personal taste and opinion. This is especially true in a pop culture question such a this one. It would be acceptable to say that Fats Waller was one of the greatest Jazz composers of all time, which means he is clumped in a group with others, but to say he was the greatest again open to debate.
No question Fats Waller was a great jazz composer, but the greatest ever should go to someone like Duke Ellington or Thelonius Monk. Fats Waller was overlooked for a long time, and that makes it tempting to say he was the greatest ever to get his name out there in the public, but he was not the greatest.