Perhaps someone could release a source code app that fills this gap.

Apple provides the tools to sideload software you build from source in Xcode, whether it’s your own code or someone else’s.

You have to use a Mac, and with an unpaid account there are limitations like app signing timing out after a week.

It’s much more hassle than the App Store, but you can run whatever you want for free if you build it yourself.

I know it’s not the same as ‘download app and tap on it’, but it’s possible. iPhone developers do it all the time.