All those men want to talk to her. She decides if she wants to reply to them or just ignore them. I would find it odd to claim the men were holding the power in this situation.

The neat thing about Tinder is that nobody has to assess those first-contact messages, they just swipe people they think they'd be interested in and if they both like each other, they can talk. I've never used it but I'd say it's probably equalized a lot of things--men no longer spend all their time carefully composing introductory messages only to be ignored, women don't (necessarily) have to sort through hundreds of "wanna fuk?" messages to find the decent ones.