Being an introvert myself and perfectly fine when being alone, this is so hard to read. Possibly it's just me but making new friends is quite overrated, and the whole thing OP does feels forced and artificial at many levels. Genuine connection should be built on mutual deep interests, and small talks at random places rarely reveal them. I'd be disappointed if someone starts a conversation with me artificially because I'm part of their hidden social experiment.

Key word: rarely

It’s a numbers game with very low stakes to the downside and very high to the upside

I thought the same thing. This was really uncomfortable for me.