I still think the man should pay if he asks out the woman. We have got a lot of customs and unspoken rules in the dating world. While many things can change about the gender roles and the economy, there are still some values to having those customs in place. If I'm initiating the date and courting the lady I think it's my responsibility.
It makes me really really uncomfortable to have my stuff paid for, especially by someone that I don't know well. I don't want to feel beholden to anyone. To make myself more comfortable, I like to pay for myself on the first date.
Always split the first date. Or better yet, don't even spend money on the first date. Because of how society structures men to be the ones who initiate, it's quite sexist to make the guy's pay because 'he's the one who asked first.'