Unironically, I think that this could happen soon.
That sounds crazy, but here me out. Pretty recently there was an announcement regarding a streamer service, that would allow people to play Fortnite, from their phone, through a mobile safari
So, in order to block fortnite form being played on an iPhone, Apple would literally have to do what you are suggesting.
So no, they are not going to block websites.
Apple has always clearly stated that this is perfectly fine on websites, just not in apps.
Alright, and fortnite is now going to be playable with in web browser purchases, on the safari web browser pretty soon.
So the purchases, without going through Apple, are going to happen on the iPhone, as well as the playing of fortnite on the iPhone.
And Apple would have to prevent certain websites, if they wanted to stop those purchases that go outside of Apple's app system.