Congratulations, you've just reinvented the desktop adware / malware market. We know that if this is possible users will be manipulated into making bad decisions which are hard to recover from, and in many cases those bad decisions will be made for them by their carrier.
What I would support is that the app store should be more open: no refusing apps for competing with the built-in apps, and removing the ban on purchases which don't go through the platform — let the store owner charge for payment processing but e.g. Amazon should be allowed to sell you a movie on iOS without paying Apple a cut simply by using their payment system instead.
Also, is Android as malware infected as GP describes? He singles out desktops, but Android does allow side-loading apps and people still near exclusively download apps though the play store. Adding a few other stores of big&trusted companies to painlessly load apps doesn't seem that risky to me. But would certainly add competition. I really don't understand why I must have a Google account to download Microsoft office.
> I really don't understand why I must have a Google account to download Microsoft office.
This is a related but separate issue: most of the value comes from trusting Google to verify that the app you found searching for “Microsoft Office” is actually published by Microsoft. Having a Google account saves you from having to manage accounts with every software publisher you use — which is huge for most people — but it's not really a prerequisite for user safety the way having a review step makes it a lot harder to spam popular application names.