Sad news. But as you said..., he has not looked well in recent years. I'm a huge Eagles fan, and absolutely loved 'The History of the Eagles' documentary.
I do not share your view on Glenn Frey as it seems to me that the 'Take It To The Limit' argument was more of a 'last straw'. Just like the Beatle who did not break up because Yoko sat on an amp. It wasn't just one thing. As for Meisner, he had already let it be known that he was tiring of the touring life and other things. He was already considering leaving. He wasn't kicked out like Don Felder was.
That being said, Frey was a bit of a dictator, and I suppose he could be a jerk too. But Don Henley said himself, that the band wasn't a democracy... there were 2 main leaders... period. And though Frey & Henley didn't always agree... there was no way you were going to get the whole band to agree on things. And as it was, they were/are a huge success story.
Anyways... Randy Meisner was a great singer/songwriter, and bassist. He was perfect for the Eagles while he was there. I admired him, and think it is very sad that he has passed.
RIP Randy.