Paying doesn't work --or at least decreases your chances of closing the deal-- because it's part of the whole pathetic, supplicating, please-like-me, I'd-do-anything-for-you, niceguy act, and that's just plain unattractive because it signals scarcity mentality and low value.
It also increases the formality of the date (like, "See? This is an official date. We're playing by the rules of it!") Nothing kills attraction and creates the brother-sister vibe like such formality.
Also as you said, it does put your firmly into 'provider' territory.