Also, with Steam's push towards Linux support this would be a dangerous strategy for Microsoft. Gaming is what drives a lot of people to Windows over other platforms. If Microsoft actively makes Steam unusable on Windows there's no reason to think people won't just seek out a better platform for Steam.
Similarly, a UWP app could conceivably be allowed to trigger the install of another UWP app, but it would pop-up a Windows box, not unlike a UAC elevation prompt, showing the app name, publisher if properly signed, and requesting the user permission to go forward with the install.
IMHO, I expect Microsoft to release a solution more like Apple's App Store and less like Google. Clearly, Epic Games' founder has the same concerns. He's also expressed concern with Microsoft only allowing something like Steam to be installed via side-loading, which he thinks provides a barrier to entry that is too high. I tend to agree, it's easy to slowly make side-loading more and more difficult as time goes on, or to make more and more critical APIs unavailable to non-UWP applications.