It's been done, I know of a couple of these. They start out well intentioned and end up being backseat drivers in every company they launch, usually with bad side effects.
Having seen this model before, I think the challenge there is incentives, motivation and focus. If you have a winner, it's likely that through power law effects it makes sense to double down on it unless you have too much capital to deploy through that company.
With that said, I think running a product studio before you find product market fit or the killer company is not a bad idea, especially if you can work directly with LPs to source the funds. Then the challenge is just making sure people don't step on each other's toes when you staff the winner.
I'm increasingly convinced that very few products need to be companies, and the insistence that they do is why a lot of them end up so shitty.