Apple and Microsoft only have licensees for their closed ecosystems. For Microsoft, that's the windows store and the Xbox platforms. For Apple, that's just iOS (as far as I know).
Consider Steam, itco.io, GOG, Desura, and the like. These are sales platforms that run on Windows, Linux, and Mac OS. If Valve, CD PROJEKT RED and others had to pay to put their shops on Windows, and then also pay Microsoft for putting the games it sells onto Windows too, then that would be quite an accounting nightmare. This is also why there is no Steam on PlayStation, or Xbox.
The only case I know of where an app has been able to provide its own software from inside a closed ecosystem has been the success of the Amazon app store inside Google's platform.
As to Quality control, it varies massively.
Consoles such as PlayStation, XBox, and Nintendo devices, have very strict guidelines, and go through an official process to be approved to go in their stores.
Apple has a much more lenient process for the App Store. The same seems to go for Steam, and other Desktop PC store fronts.
Android is pretty much "check for viruses and other dodgy stuff and publish."
Publishing a game without a middleman or vendor gives you the freedom to decide for yourself, and can often still lead to good quality software (for example, Adobe doesn't go through a certification process, but no-one is going to say their software is half finished and untested).
As to costs and the publisher cuts, some of that stuff is corporate secret, so not safe to divulge, but there's a lot of public knowledge that states numbers around 30% cut on the secretive platforms.