Pretty sure that Corgan hired Byrne because Corgan was going through a mid-life crisis and thought that hiring a 19-year old would add some youth to the band's image so that people wouldn't think of SP as some "old '90s band."
Didn't work. Just made it look like "some guy clinging to his old successful band name, playing with a bunch of glorified session musicians, and calling it 'Smashing Pumpkins.'"
Byrne's biggest sin was "not being Jimmy Chamberlin," I guess. There's nothing particularly wrong with him. He was definitely not the worst thing about the Smashing Pumpkins at the time.
In fact, his own math-rocky musical projects probably have 1000x more creative merit than Corgan's output of the past decade-and-a-half. At least the kid just plays music because his heart is in it, not because he wants to be on MTV again.