There is no reason to change the convention. It only applies to the first date. Without it, people who don't know each other have to show more about themselves before they get to know each other than the should have to show.

The underlying psychosocial issue is rejection and learning to handle it. Under the conventional way of doing things, the man risks explicit rejection and the woman risks implicit rejection (by not being asked out). Both sexes need to learn to deal with their form of rejection. Havng women ask men out doesn't "flip the script." It just expoises both sexes to an added form of rejection. How is that a good thing? So the convention endures, and the asker pays for the FIRST date. If you believe, as I do, that not being asked out is a constant form of rejection for a woman, then the man paying for the first date seems like too little compensation for that, let alone for sex.