I assume that Google Play is a big source of Android revenue for Google, and a major reason for them to keep developing it.

It's even simpler than that: Allowing others to dictate the terms of interacting with users would be very bad for Googles bottom line. What happens to Google Maps dominance without knowing who's going where (for new/closed shops) and how fast (for traffic information)? What about Chrome pushing users to install on desktop, Photos being built-in, and basically every other Google property being the built-in default? Android reports so much information it means Google will, IMO, always and forever have an edge over every other advertising company.

A large part of why iOS has a perception of quality is their handling of the app store.

For a frankly shocking length of time, basic actions like installing a well-rated flashlight app from the Play Store result in your lockscreen being replaced with ads.

Apple on the other hand was pretty ruthless about rejections.

Technically AOSP ("bare Android") has no reliance on an app store, but having someone vetting apps and providing ancillary services through it (Google Play Services) is so valuable that manufacturers are willing to give up a lot of control.

So that granny hasn't 5 toolbars on Internet Explorer and a couple of RAM compression tools and registry cleaners.

Love Windows store and S mode.