I think "the guy pays because he has a penis" is a meme that deserves a quick, painless death. "The guy (or gal, or the person who asked for the date) pays and expects sex in return"...that's not a date; that's a financial transaction.

The rest of it...I've moved over time from doing everything strictly dutch (date or not, but there was a period where drcpunk and I were passing a symbolic half-penny back and forth to aid in splitting the cheque) to mixing up a split and a treat (and tending to let treat move around between trading off, "the person who can afford to pays," (of which "I'll treat because I want to eat out well tonight and I want to hang out with you, so don't worry about it" is one variation)).

Regarding power dynamics...you can actually take those either way (regarding paying, anyway; I think it's harder to sexualize ordering in a fashion other than "the dom orders"), so I see no reason to have power dynamics induce such an unfairness in a relationship I'm in. To consensually take advantage of an existing reason for one person to pay, sure (although that's a minefield, for I hope obvious reasons; similar to the distinction between "I'm hurting you because I want to" and "I'm hurting you to punish you for failing a test that you were rigged to fail").