If there is exactly one global service that does all the checks for every single internet user, which every single website uses, and the information going through them is always known, then sure, they could certainly block stuff.
But it's quite clear by now "we aren't going to implement age verification on the internet" isn't going to happen, that verification is going to be implemented eventually, and in the rather near future. And places like the UK and many US states are extremely unlike to roll back the already implemented solutions.
So the question now is how it can be done with the least amount of invasion to privacy, and crucially, without the website needing your actual ID.