Another perspective is if it isn't that important, there's little need to read it, much less going out of one's way to bypass a paywall.

This is a fine thought by itself. As long as you don't imply that anyone doing an unimportant action is behaving incorrectly.

In other words, someone that says "I don't care much but I looked anyway" is not a hypocrite.

"I have no interest but I showed interest" Strikes me odd, and should likely be confusing to an observer. It seems an oxymoron which is somewhat analogous to hypocrisy

Only if they say they have absolutely no interest. If they just say it's unimportant, or not worth paying for, there shouldn't be any confusion.

Relatedly, I think it's worth 0 cents to go flip my phone over on the table. But I'm going to do it anyway.

You mean cure FOMO? :D