This… is a pretty terrible idea.
It adds nothing to the core QA experience, and doesn't serve the core goals of SE. It doesn't help add to the knowledge base, and is kind of the lowest common denominator feature. Also - one of the sections of our help pages says "this is not a dating site".
While Careers and such aren't Q&A — they're of use to SO's core audience, and a proven money-maker.
Running what's essentially a dating site is problematic. We're often not had the best experience with people trying to use chat to pick up other users (it happens, and is terrible): some people are mild creeps, and we've occasionally had folks just go full abusive.
Quite frankly — that's not what SE is about and we'd need a different set of expertise to actually manage such an enterprise. Its probably going to cost more than its worth to run, and the potential downsides aren't worth it.
Lets leave the matchmaking to Tinder, iCupid, and my aunts. Or whatever the cool kids use these days.