Considering Wesley was Gene Roddenberry's self-insert character, I think the idea was to establish that as brilliant as Picard is, there's still someone who can get his goat by virtue of just being that special.

That makes sense. It could have been an interesting dynamic, if they had committed to it and followed through on growing their relationship from bad to good.

I suspect the "everything must reset in case these episodes air out of order" effect can't have helped with making it work.

And then also, it's just hilarious that Picard is that far into his career, and an enlightened 24th century man, and still occasionally just "punches down" at his girlfriend's kid who isn't even an ensign. Haha.