I'm with you, but see a million obstacles (aka. reasons for why things require payments).

You would need some form of moderation, to weed out illegal content as well as simply bots, spam, and dead profiles. Also for message content. I've given it some thought and suspect it can be crowd sourced to some degree, but also needs counter balances. Instead of limiting a profile to be live/banned, you could have a percentage score of peer-reported subjective legitimacy (ditto for message responses, heck you could even have a section of outright reviews of the person's behaviour - although that, again would be subject to abuse and moderation).

Hosting, traffic, etc. would be an unavoidable cost, but can be mitigated with low resolution photos (VGA should be "good enough" for an initial impression, no?)

For sure, an open source solution would offer way more fine grained filtering.