What does any of this have to do with YouTube blocking PIP?

Simple, it means that if the browser would decide to force YouTube into allowing PIP, that would be the browsers legal (and moral right).

Additionally, there’s a precedent that users want to be able to control what a site does, and are willing to take extra steps to achieve this, so a browser should implement such functionality ideally in the first place.

There are already numerous examples where browsers intervene to stop user-hostile pages. The reason pop-up ads largely don't exist any more is because browsers intervened to kill them.

Exactly, and the same should happen here. Users should be able to force PiP.