I think that you should be able to install your own app store like fdroid which doesn't require a sign in.
In a few years: You want to play a game? Fine, let's bing it in Safari and play right there.
"there's an app for that" soon will become "there's a web app for that".
Android has problems of its own though. Yes, you could install apps easily without access to the Play Store. But most Android apps rely upon Google's Play Services one way or another, so those apps wouldn't work properly, if at all.
Only when I download I paid app do I want to identify myself so that I can download it again.
It's my device, not Apple's or Google's, so I should be able to download a third-party app without identifying myself to the app store owner.
In my last comment, I did not ask for iDevices to be able to install apps from outside the iOS app store.
Quite a lot really.