> unless the phone is rooted.
That's absolutely not true at all.
All that happens is that, the first time you try to install from such an application (or any other application other than your store, eg: the first time you try to install an apk after you download it from your browser), a settings windows appears telling you this application can't install more applications on your phone until you give it permissions. From there giving the permission is a two click matter, and you don't need to look for it the link is given. See the exemple 2 pictures (and that's the only two steps - note that the "settings" button in the first takes you directly to the second picture, aka straight to the right settings page for the correct application, no looking around needed): https://imgur.com/a/Vafqyic
Then you press back one time after giving the permission, which is the normal way to go back to what you were doing on android, and it works at expected, aka it goes back to the install screen except this time it enables the install button.
Any porn site like youporn and pornhub, or epic with fortnite, etc ... Do it this way with no major issue, because the messages are super clear, and where to click to allow it is super clear, no need to look for it.
If anything, this is almost too easy and I'm surprised there is not a bigger spread of malware through browsers using that, and I would be for it asking you to confirm your password before enabling that permission.
EDIT: it appears I missed that parent was talking about UPDATING apps, not installing.