I hear that a lot but I don't think someone like Bret would have had as hard a time adjusting as people seem to think. I'm not quite sure what "he was a wrestler first and foremost" means really.. that he didn't do entertainment as much as he did focus on the in ring product? That's true, but I can think of others that were like that that fit pretty well during the attitude era. And either way I would bet Bret would have had a larger impact with the last few years of his career with Mcmahon than he did in wcw.
I just think WWF made a mistake in letting a guy they'd built up since the mid 80's to world champion status go in his prime.
Bret Hart went on Off The Record and publicly said he hated the way the product had gone in WWE and this was in late 1997 before a lot of things happened through early 1998 to late 2000 so Bret Hart already stated he couldn't work in WWE with the way it was. The company was being built around Stone Cold Steve Austin and Shawn Michaels as they were the two men who personified attitude and edginess and it drove Bret Hart mad as he had felt pushed aside for a year and a half and couldn't accept not being the top guy.
During his run as top guy in between 1993 and early 1996 everything was built around actual wrestling and basic storylines which suited Bret Hart perfectly because he was a great in ring worker and a great storyteller in the ring but as a mic worker and character Bret Hart struggled. The basis of The Attitude Era was character and storyline driven with a lot of edge which is why people like Stone Cold Steve Austin, The Rock, The Undertaker, Mick Foley, Triple H, Chris Jericho, The New Age Outlaws, The Hardys, The Dudley Boys, Edge & Christian and Vince McMahon were all so successful during it's entirety as well as Shawn Michaels briefly but Bret Hart wouldn't have done.
Had he been booked properly in WCW then Bret Hart would have been very successful there as well because their product was very family orientated from 1998 onwards which would have suited Bret Hart perfectly. Unfortunately too much power was given to wrestlers which meant younger or more deserving wrestlers never got the opportunities they should have done with Bret Hart being one of them. As Vince McMahon himself said Bret Hart was someone you could build a company around in the right setting but The Attitude Era wasn't that right setting in any way at all and everyone knew that which is why Shawn Michaels was the one Vince McMahon went with once he knew he had to change the product.