You wrote a comment upthread that misapprehended the post you were critiquing. I was motivated to offer some corrections. I'm less interested in the philosophical argument you now propose, except to say that PII segregation has only very rarely been the reason I've seen people adopt stateless tokens. It is still easier to segregate data using stateful token schemes than with JWT.
But I don't want to pretend we're still having the same conversation that started up thread. I assume you take my point, that if you think "I already have to do JWT so I don't save anything by not using them everywhere" rebuts the post, you've misread it a bit.