We got here rather simply... Apple introduced the iPhone with no apps at all, then gave a half-assed open solution (bookmarks on your home screen, essentially), then they introduced the App Store, with their rules. Since there was no other way to get apps on the phone (short of jailbreaking), App Store won and Play Store was built in this model.
Other smartphones in this space at the time (Windows Mobile and Blackberry) didn't quite capture the imaginations like Apple did. WM was fairly easy to sideload apps to; not sure about Blackberry.
Unless they've changed it recently, you can install anything you want on an Android phone. You just have to change a setting to allow apps from unknown sources. It takes a few seconds.
I believe this is still the only way to get the Humble Bundle app/game installer on your phone. https://www.humblebundle.com/app
Play Store itself behaves similarly to App Store. Android lets you sideload through a separate mechanism, and all Google has to do is remove that switch from Android
They could do lots of things, but absent any evidence that they're likely to, it's just wild speculation.
And it's not "sideloading." There's no other local device involved. Once you've flipped the "unknown sources" switch, you just go to a website, download, and install, same as you would on a desktop.
Other smartphones in this space at the time (Windows Mobile and Blackberry) didn't quite capture the imaginations like Apple did. WM was fairly easy to sideload apps to; not sure about Blackberry.