Not everyone has caretakers, unfortunately, but everyone needs a phone.

Then they can have flip phones. Those are still made and are great for children and other people who aren't capable of caring for themselves.

Or maybe when you buy a phone you can pay $5 extra to get the OS build that allows sideloading, or make it cost $5 and require you to hand-sign a bunch of forms to upgrade an existing phone to a sideloading-capable version. A little extra friction at phone purchase time (rather than app download time) would likely steer most people, especially non-techies, toward the safer option. Sure, maybe it doesn't stop the problem completely; someone completely bought in to some scam may go through the effort anyway. But if someone is that gullible, they're pretty destined to be scammed out of their money no matter what the protection.

Why should people pay for the privilege of installing apps without having to submit their personal record to an American mega corp which then vet what they install?

You have the issue reversed. I should people should be able to buy specifically locked phones separately if they want to. Actually they already can.