Remember that Apple does in fact wield a level of coercive control here. They can ban any app or entire developer they wish at any time. But they do want a solid amount of development going on overall, despite individual exceptions. So just like a real world legal system, there's a dynamic set of cost/tradeoff equations, and practicality/reasonableness really matters. If Apple provides nothing and insists on nothing, the economic incentive to either cheat or simply leave entirely may move to near-requirement for too many developers. If Apple left it as "do whatever" and then slowly added requirements, it's still much harder to police and drive solutions that compromise best.

Offering something official that is less effective then the previous ones but still of enough use to be valuable and also has the advantage of official support and sanction, then blacklisting anything else raising the economic risk, is a fairly tried and true strategy that can be reasonably effective overall. Cheating is disincentivized for those who are legitimate and the search space is reduced, making it turn easier to further enforce. Apple's exact compromise could use more tweaks from the sound of it and evolve better, but the basic concept of "better to have someone troublesome inside the tent pissing out then outside the tent pissing in" seems to apply here too doesn't it?

Furthermore if many users are also more alright with it that too by itself can be a positive, preventing an arms war. Sometimes situations like these can fall into a vicious spiral left on their own: there could be many devs or even advertisers who would prefer to go with less obnoxious and creepy practices, in turn provoking absolute counter attacks, but can't disengage unilaterally when their competitors don't think as long term. Having a higher entity step in and force uniformity won't even make them all unhappy.

They're in a position to say 'you must use our Ad-ID, and if you don't and we detect you tracking users by other means, then your app will be rejected'.

And as it happens, that's what they do, when they introduced IDFA they started rejecting apps that use other tracking heuristics, including the old UDID system.

Screen recording sounds suspicous and even illegal in some jurisdictions. For example, if an app records my screen while I get an incoming iMessage, I can easily argue that being a GDPR violation.