F-Droid.org?
There's also Ad-hoc signing, which I believe is longer-lived, requires a developer account, but has restrictions on how many people you can send it to.
As an enterprise user you can also distribute apps yourself to company employees without going via app store verification, though I think it's much harder to get onto this program https://developer.apple.com/programs/enterprise/ . This is what has occasionally been abused, I don't know how the certificate is revoked centrally though, but it's not for [user] self-compiled code.
It's possible that my knowledge of this is slightly off, because it was a few years since I worked with this stuff.
- your typical user wouldn’t know what to do with it
- every install would run only for a limited time (only apps distributed through the App Store have a certificate that doesn’t expire), so those users would have to reinstall the app every week or so.
- it would make it harder for them to make money from it (they would give away the game for free. The in-game store wouldn’t give away stuff, but the source likely would soon be changed to support alternative stores)
It's not really an alternative to an app store. There are also enterprise signing certificates for distributing custom apps within large companies without these restrictions, along with cases in the past where people have abused this to distribute; these are usually shut down pretty quickly as a blatant violation of the licencing agreement.