I thought about sth like that too because I was annoyed of searching all these apps in the play store, this was ok, when the apps are not in Google play you had to seach for apk. Soy idea was a public git repository where everyone can pull his APK. The next step isn’t that difficult, a git client that checks maybe every hour if there are changes, it will pull the folder and automatically open the APK with the apk-installer and install it. The last step would be to remove the old app.
This app would make Shure that always the latest version of the apps will run on your system.