I do think its very important for the guy to pay for the first date. Otherwise the guys isn't sure what is going on.
Is it a date or does she just want to be friends? Did she have a bad time? Are we giving off a strange funk? Inquiring minds would want to know lol . ..
It can be a good way to qualify if it is a date also.
One time I was out with a lady and she was pretty form about wanting to contribute and I responded:
"Well, since this our first date gorgeous why don't you let me cover it? This is a date isn't it? (when she blushed and said yes) I said if you really feel like covering the next one its up to you."
Went over rather well. . . I am trying to remember if I ever called her again though alas
lol.