These toolbars were usually bundled with legit software (Heck, even Java installed Bing toolbar..) behind dark patterns where a computer beginner would, understandably, not realize they were also installing something else.

As long as the dialog for unlocking your phone would clearly state the risks and what it does, unlike those toolbars upon installation, I think it would totally be OK.

Imagine if you couldnt install Linux on any PC because Dell didnt give you the keys to prevent you from hurting yourself. Or Apple didnt allow sudo in macOS. Seems kinda absurd right? Yet this is the standard for phones.

Also Id like to point out that Android allows installation of external APKs (after activating) and it didnt lead to a super increase in malware, as user still prefer the Play Store, and APK are usually left for the more technically inclined user for niche purposes or often times Region lock circumventing.