Should phones have something that shows your profile to people in the proximity?
The whole idea is a privacy minefield, so it would have to be very carefully designed and implemented, of course making it opt-in. But still, should we even pursue this idea?
So that, for example, even if I met someone just briefly, they can still later see the contact information that I am willing to provide.
Wouldn't that make it much easier to connect with people who live close to you?
Are there any relevant projects or ideas that already exist?
This isn't exactly what you're going for since it isn't automatic, but Apple is introducing NameDrop in iOS 17 which will allow you to share contact info by holding iPhones next to each other (similar to Bump back in the early 2010s). Of course NameDrop is closed to Apple devices which sucks (Android has Nearby Share, but it doesn't default to sharing your contact), but the idea of being able to hold phones to each other to share contact info would be ideal for me - it'd be quick so I wouldn't have to think about it and would be willing to do it for brief interactions, but also ensures my info is only shared with who I choose.