I find this a pretty weak argument against the tl;dr. "tl;dr" has become a noun, that means one-line / extremely short summary. Language sometimes grows like that.

A better argument against the tl;dr would be that the piece you're writing it for becomes redundant, provided it's an accurate tl;dr. The term tl;dr wouldn't be needed then, because the tl;dr itself becomes your piece.

If it isn't an accurate tl;dr, there's no reason for providing it in the first place, except maybe for giving a rough idea of what your piece is about. OP rightly points out, though, that conventions already exist for just that. A descriptive title or an introduction clearly distinguishable from the rest of your piece, for example.