This gives him an opportunity to show her he is a success. She will see him spending lots of money and not caring if anything costs too much. A man who has a good job can afford to do this. If he has a problem for paying for a date he will appear to be a loser, thus he won't get in to her pants.
Like it or not, some things remain the same no matter how much other things change. Seeing tend to have skills and abilities more tuned to providing for the family were women tend to have skills and abilities more tuned to nurture the family. To demonstrate their ability to provide, men tend to be the one who pays for dates. Another typical thing is for women to make food for the man later in the dating process. Thing is, women will always be the one to give birth, so the man should be able to provide for the mother of his kids.
Men paying on the first date would be a very lovely gesture. Hell, women paying would be just as lovely. The couple could split the bill or even take turns paying for dates. It all comes down to the couples choice. The man doesn't have to pay for the date. It's just the couples choice.
The entire construct of men having to pay on a first date is based on outdated societal norms, men courting women, women being the "weaker" gender, these are all old-fashioned stereotypes that we should break out of. A date is a mutual decision between two people, and men are not obligated to pay for the first date.