It's talked about as being a place where relative strangers socialised and had substantive conversations on politics and philosophy that changed the history of ideas whereas today they are places to be "alone together".
My best guess is that clientele were so filtered by opportunity/access such that they resembled a business cafeteria or a private members club more than a public venue. I guess the closest thing today might be a subject specific meetup. I suppose that if trying to recreate one, you might want to base it around the service of a novel stimulant that can't be found elsewhere that encourages frenzied socialisation. MDMA cafe anyone?