Well, the real problem with notification screen imho is that it is integrated in the carousel and pushes apps to background if selected.

You can already have kind of what you suggested by applying a patch that maps swipe from left edge to notifications to have it accessible everywhere

Changing the way how to reach it does not solve android apps being paused and the need to reselect last used app.

Yes, there is a patch "bring back last used app" when leaving notifications, but that shows homescreen briefly while changing back and does not solve the app being pushed into background in the first place.