The main issue here isn't native apps. It's the existing framework for installing them.
For instance, would it be that far-fetched to be able to open an app in a single click?
Current extended process: 1) Click link that takes me to app store page 2) Find and click install button 3) wait 4) Click "open app" button
Streamlined process that accomplishes the same: 1) click link 2) wait 3) app opens up (download/install hidden behind spinner)
Even if you have to add a pop-up in there to display permission requests, it's still a much smoother experience.
You'd have to worry about app sizes but that's a solveable problem as well.