There are many popular app stores on Android and you're free to use any of them (or none of them, if you just download apps directly from websites) without rooting your phone, jailbreaking, etc.
From the perspective of an Android user, a lot of the alternatives are interesting. Especially F-Droid.
From the perspective of the app developer, it doesn't work. You use Apple and Google or you lose 95% of the market.
And the same constraint keeps it that way. You lose most of the Android market if you're not in Google Play, so nearly everything that isn't explicitly banned can be found in Google Play, so most users have no occasion to install any other app store and the friction to developers using another one to the exclusion of Google Play remains high.
A recent list of someone's favorites: https://42matters.com/blog/?p=the-best-of-2020-a-list-of-app...