You partly answered your own question: With the floating thumb, you don't need to use other fingers for muting strings because the thumb is doing it.so what's wrong with anchoring my thumb on the E?
I never thought about it so I film my playing and it turns out my thumb tests (with no tension) on the E whenever I'm not playing it. I mute the E with my thumb and all the other strings are muted with my fingers.
I think the other main reason is to ensure consistency of attack across strings. With the floating thumb or moveable anchor, the position and shape of your hand, as well as the angle at which your finger strikes the string, is exactly the same no matter which string you are playing.