Your list is better than the VH1 ranking, that’s for sure. If it’s influence for all time, then it would probably have to go: 1) Bach, 2) Mozart, 3) Beethoven. I’m surprised you didn’t put the Rolling Stones or the Who in the honorable mentions. Also, I’d probably rank Stevie Wonder higher than Jackson or Prince considering how much he influenced them, if influence is the criteria.
In fact, if they were doing it by influence then 50s and 60s artists should get more weight considering what they shaped, so Chuck Berry and James Brown would deserve a lot of weight by that criteria. So would the Beach Boys and Traffic.
But here’s another thought — influence in terms of what? Performance? Musical Vocabulary? Vocalizing? I think they need a better criteria than “influence.”