Interestingly, Apple already has 99% of this in place on iOS - if you have a "child" device in a family share account (maybe not the right word?), the "parent" has to approve even free app installs on iOS. Child hits install, it triggers a push message to the parent account to authorise the install (via touch ID/PIN).
So while it isn't quite there for authorising all unsafe activity (in fairness, maybe it is, perhaps I didn't find the options yet), but it certainly lets you control app store installs. In essence it feels like a personal version of lightweight MDM.
It would be straightforward for this to be extended to "Name wants to enable installing apps from outside the app store. This means you won't be able to approve what they install. Allow this?"
To me, if Apple were to allow sideloading, it would be controlled via this route, and manageable by MDM policies as well (so managed work devices can't run sideload apps).
I was also reminded how in the past if you got your phone from Vodafone it would be SIM locked and after your contract expired you could not use the phone on other networks, you had to find a phone service to unlock it, I am not sure if it was a national law or EU law that demanded that unlocking should be easy to do when the contract is over(you should ask for it and you should receive a code for free). With Apple you pay for the phone, you own it but you are still locked, we need a similar law that if you own the phone you should be allowed to unlock it.
If your mother is not that "technical" do you think Apple is so incompetent they could not make the enabling of side loading complex enough so is hard for this group of people to activate it? I am just 1 person and I am thinking at possible ways to do it for 1 minute and I have some solutions, Apple could do better.
Apple could create a "kid mode" that you can enable on your less technical family members, it could require someone else to authorize "unsafe" activity. There are solutions and is obvious that if the solution is for Apple interest is always found if the solution is against Apple interest is never found.
Other solution is to allow side loading only in EU, let EU people have the choice to be scammed or tricked to install apps that use the evil GPL but keep the US citizen "safe". Apple has done a lot of things to sell in China so doing different things for different markets is not something new for them. If this happens we can also then see the numbers and determine how stupid or not are the EU citizens that unlocked their phones but I have a permonition that even if things go well in EU I will see the comments that US is special, in US it will not work.