If one verified app can install many unverified apps, either aurora droid or fdroid basic or one of the many other frontends would end up offering that feature quickly.

But there's been some comments that even that wouldn't be possible, every app would have to be verified individually, or be signed by a developer with less than 20 installs.

(Which of course then begs the question: Why not build a version of Fdroid that generates its own signing key and resigns every app on device?)