That's not what protocols are for, though. It would still be served over http, so what you're looking to replace is actually the world wide web, or www. In other words, http://app.microsoft.com is what you meant.
These are already possible by retrofitting existing technology but the question being asked is what would a reimagined, more app friendly web platform look like.
Maybe https+app://microsoft.com is better? (plus signs are valid in uri schemes)