I don't want to sound cheeky but Morrison wouldn't have happened if Jason had his own universe
(Or Battle for the Cowl for that matter and some other stuff that I'd rather forget.)
It also wouldn't be the first version of Jason that didn't meet Bruce. It's rare but neither Father Todd from the Flashpoint universe, nor Jason from Gotham City Garage ever met Batman. Bombshells Jason met Batwoman instead of Batman (I'm not sure if Batman even exists in that universe).
I don't think it would erase Jason's whole history by exchanging some people (mainly Bruce and Joker because Jason doesn't have any deep/consistent relationships with anyone else in the batfamily - so what does it matter if those characters exist or not?) with new characters who fulfill the same purpose - but better because there's only one writer (at a time) for all of them. One of the biggest problems with DC is that too many writers write the same character. Too many cooks spoil the broth. Too many writers ruin the character/universe. It's already hard to find organic stories and character relationships in the DC universe but Batman especially doesn't really feel like a character anymore but more like an empty vessel for whatever kind of story/personality the writer wants to create.