No, we can't solve the problem that way: the very same problem wound remain: EU and 5/9 Eyes want e2ee backdoored or gone. If you start legislating which apps are allowed, you're putting yourself even more at mercy of gov regulation.

And the regulation would be blanket, with little to no way of sorting things out through unofficial channels as it can be done with Google. It'd be "backdoor or jail", not even sideloading apps to help you.