[pynappo]

the "rent" in the saying is the effort to learn and upkeep a certain piece of knowledge in your head, to the point where you can recall it as needed

living rent free generally means that you are able to easily recall a piece of knowledge (and often do, even if you don't want to).

something that pays rent might be like an important concept for an upcoming school test, for a class you're not interested in.

[strken]

I always thought rent was utility, and a piece of knowledge or an opinion that didn't pay rent was one that provided little or no practical benefit to you.

The term in its original use described an obsession with a particular group or thing and called it out as pointless. I don't think it would make sense for rent to mean effort in this original sense, nor in the broader way it's used here.

[junon]

I have no idea what pseudo-intellectual discourse this is trying to be but the phrase "X lives rent free in my head" means only that "I think of X a lot because I enjoy thinking about it". Nothing more.

[strken]

Go read https://knowyourmeme.com/memes/rent-free and learn the origins and predominant usage of the phrase.

In addition, it literally says "rent free". There's nothing intellectual or pseudo-intellectual about reading the phrase "rent free" and concluding that the information does not pay anything to live in your head. This is basic reading comprehension.

[junon]

JFC nothing pays rent to live in your head. I don't see the point of analyzing something so literally, completely sidestepping the content of the article in question.

Get a hobby.