The solution is to integrate sideloading into the parental controls. There are already existing permissions in iOS to restrict the installation and deletion of apps, so adding a sideloading permission should be straightforward. (They can still leave it disabled by default and bury it a bit behind a few menus and dialogs...) If a family member is really so technologically inept they can't be trusted with their own phone, then you should already be making use of parental controls in some fashion. Set a pin for them which you know and they don't know. It's as simple as that.
Perhaps that's a bit harsh, but we should not be sacrificing these freedoms at all, let alone at a time when there are already existing solutions for protecting those who are vulnerable.
(The relative simplicity of this solution is yet another piece of evidence this issue is not really about the security of users.)
Play integrity doesn't protect anything, disallowing side loading has no security benefits. Thats just a lie, a convenient piece of propaganda to convince you to advocate against yourself.
There is no security on the play store. Can apps ask for way too many permissions? Yes. Are they open source? No. Are builds reproducible? No. Does Google check the code? No. Is it almost all adware and spyware? Why, yes!
Google does not give a flying fuck about the quality of the play store and anyone who disagrees is legitimately delusional. Have we looked at the play store? Seen what's recommended?
I mean, for fucks sake you can't download a goddamn calendar app without it asking for phone permissions and showing you popup ads.
Look - Google allows malware on the playstore because they have to. They make money off of ads sold on the playstore and advertisments in apps. Google has ZERO incentive to stamp malware. But they have every incentive to prop it up.
I don't need Grandma to download an unsigned binary from the internet to compromise her. Get fucking real dude. I call her, ask her to install anydesk, and remote control her device, all Google approved.