GoG does it for a small, rotating selection of titles, which is good. But for it to make a significant difference, they'd need to be able to move a large majority of people's libraries. That's much harder, given the variety of developers and publishers you’d need to strike deals with. I don’t think it’s feasible, sadly.

GOG still does from time to time. I check this weekly: https://www.gog.com/connect

Edit: You can insert some EA keys from Steam into Origin: https://pcgamingwiki.com/wiki/List_of_Origin-redeemable_game...

I wish EA (and other distributors) did something like GOG Connect. IMO I'd be less annoyed if Epic offered something like this for current Rocket League owner in order to keep the userbase as big as possible before they ultimately split it in two.