I like all of their albums with the exception of Final Cut. But it's because of Final Cut that I like post Waters stuff. Waters brought the post tonal, even the bizarre element of Floyd to the table. It's because of this atonal style of his that Pink Floyd is such an transcendental enigma of modern music. That said, despite what he might think of himself, Waters couldn't come close to this success on his own. By The Wall it was clear that his ego and his delusions were beginning to catch up to him as tensions mounted in the band. While Final Cut was the outtakes of The Wall, it showed that he was out of creative juice and too caught up in his own delusions to make another quality album. In my opinion, Final Cut should have never been released as anything more than studio outtakes that are featured on a "making of" special about The Wall. So because of this the band had to distance itself from Waters if they wanted to be commercially successful. The creative energy that Waters brought to the table that made them such a huge success had dried up. There were other external factors such as the rise of punk over prog, and other things like that that also forced Pink Floyd to cope with changes.
After Waters left, Gilmour and Wright were free to explore a new kind of music, which, despite the opinions of die-hard fans, they are completely entitled to do. I think AMLOR and TDB show exactly what the rest of the band brought to the table prior to Waters departure. Was it different? Yes, but it was different in a good way. To me it was still classic Floyd in that it was very intricate music that used the recording fads of the time (in the 80s, gated reverb, cheesy digital effects, etc) in a very progressive way that would be able to stand the test of time. Look at other 80s and 90s albums of the time that used the same effects. We look back and laugh at most of them, and yet Pink Floyd is praised for how it was able to use the same effects. Fast forward to today with TER and it can be seen all over again, only this time the album is a musical throwback to old Floyd albums. Looking at the recording technology used in TER, it's clear that they did the same thing. They used modern recording techniques (sampled sounds, modern digital effects) to enhance the music. All 3 of these albums, under Gilmour's direction have shown that they were able to carry on without Waters and still be Pink Floyd. A counter example to post-Waters Floyd is Collins-lead Genesis. We all know the disaster that 80s Genesis was. Their attempt to change with the times was commercially successful at the expense of their lifelong fans. Pink Floyd was able to change with the times and still be musically viable and were able to keep the majority of their fans.
tl;dr: Waters had to go because he was going mad. Floyd carried on without him and adapted to the lineup change.