I expect the man to pay on a proper first date, i.e., he has approached me and invited me for dinner or whatever. This used to happen in the olden days, when you really only met people through friends and a first date was also the departure point of monogamy.
However, on an internet date I definitely offer to pay half or all of a bill because by its nature it's more of a numbers game.
That said, I met DH on an internet date and he paid for absolutely everything for a couple of weeks-worth of dates with lots of champagne and nice dinners - we then went on to a much fairer system that took into account our incomes.
Life is too nuanced, in my humble opinion, for something like that to 'set women back a hundred years'. Respect and equality is not built or destroyed off the back of a bought dinner. The early part of a relationship that is going places is not 'normal operation' and some rules can be suspended so that romance can roll without nitty gritty calculations. It's a bit like shopping at the airport 