A real life dating app

That's just real life. No app needed.

If I recall, there was a dating app that showed you profiles of people you'd crossed paths with that day - so, basically a conventional dating app with a novel algorithm for choosing which profiles to show you. If I'm understanding you correctly, what you're suggesting has minimal profiles; it just notifies you that a given person is nearby and that you might want to talk to them.

I can see two problems with this. The first is enforced synchronicity: I can't scroll through profiles when I've got a few minutes; if I want to make a match, I have to act on the notification right then and there. For users who live in large cities, the overwhelming majority of their notifications will occur when they're commuting, doing a food shop, eating out with friends, etc., which aren't great times for chatting up someone. The second problem is safety: users who misbehave aren't doing anything they wouldn't have done without your app, but because your app was involved, you're the one that takes the reputational damage.

There was an entirely tech-free attempt at this sort of thing called the Pear Ring, which was a turquoise rubber ring to be worn on a finger that indicated that you're single and ready to mingle. The fact that the Pear Ring website no longer exists and web searches only return lifestyle magazine websites telling us it's the future of dating suggest that it didn't work.

It would be nice for travelling...But as a woman, I wouldn't feel safe.

People tried that with the NYC subway riders. Did not end well due to creeps ruining everything good.