That has changed somewhat recently (android O I believe?). Now, when an app tries to start an installation, Android will bring you to that app's setting page wh

That has changed somewhat recently (android O I believe?). Now, when an app tries to start an installation, Android will bring you to that app's setting page where you can toggle an option "Allow this app to install other apps" or something along those lines. It's a lot more straightforward than it used to be. That said, auto-updates are still not possible without root access, I believe.