I've read about the breakup extensively. It was rather complicated and the Wikipedia discussion lack the factual depth needed to understand the situation.
Waters, from what I understand, was simply done working with Gilmore. He wanted complete control.
Waters also, as the primary song writer, felt that Floyd, as a unit, was not viable without him at the helm.
As history has proven, that was laughably incorrect; all it took to overcome his absence, in terms of revenue generation, and popularity, was to paint Roger as a villain that left in a disruptive manner. Which wasn't wholly incorrect.
Fans accepted that view, and the band was able to keep going.
That being said, if you look into the difficulties they had making music after Roger left, you see hints that his absence had a dramatic impact. I'm trying to remember the actual numbers, but the remaining members of Floyd spent an ungodly amount of time and money on the post Roger albums. Something like 3-5 times the amount of money they'd spend if Roger was still there.
The results aren't correlative with the expenditure. Division Bell did well, but it wasn't another Wall, or Dark Side. Or even Animals.