I feel like it would depend entirely on the point in the show! Like Season 1–3 hatesex would not have solved anything, but by later Season 4 into 5, it becomes quite plausible to me. My father has shipped them since the mid-'90's.

Oh, nobody was saying that it was implausible, the question was whether or not it would fix them. And, well. LOL. XD (Who doesn't ship them in some way or other? They are a thing!)