> What I’ve long wondered is how women react in the real world now that they have all the power on dating apps
Women always had that specific kind of power in real world. When/if you go to a party, observe the people who are alone, standing against a wall; they're invariably men, without absolutely no exception. This says everything about power.
Having said that, bear in mind that this kind of power is only a (arguably small) part of relationships between the sexes. It says a lot, but it's still a (small) part.
> Why would they try to find a date in any other way?
Because the dating medium strongly correlates with the interest of the people involved. Not everybody's looking for the Tinder type of relationship.
"Before Tinder", one would just go to a nightclub. It's exactly the same experience; and for the same reason, not everybody goes to nightclubs.