GoG did something a little like this. You could add copies of some games in Steam to your GoG account, by linking them—not just, like, letting you launch them through the same interface, but you'd "own" a copy on GoG, too.

I don't think it really took off. It was a little clunky and I'm not sure they got enough buy-in from publishers that the catalog available ever expanded much past their initial offering.

More broadly, I'd love to see a strict, legally-mandated separation of media distribution and production. Mostly for the film and TV industry (there's precedent—the US only very recently stopped barring movie studios from owning movie theaters, because it caused serious problems in the past, similar to how vertical integration of studios and streaming platforms is making things worse today) but maybe something similar would help the game market work better for consumers/users, too.