I think that public spaces are a great thing, and I'd be happy to see them make a comeback. During my (brief) time in Europe, it was incredible to go to a store, pick a cafe and just sit outside with friends while there's a lot of other people doing the same thing. In this case, it's probably a difference in city planning that enables it to happen in Europe as opposed to America. That said, it's still possible to create these areas. I feel that they (should) promote community, support local businesses, and also promote activity. If you do it right you should have multiple public areas within walking distance of each others.
Unfortunately, I suspect that the biggest factor is planning around automotive traffic v. planning around pedestrian traffic. That sort of public space is harder to maintain when people have to find a pay for parking for it. That's unfortunate because it's going to be very difficult to undesign our reliance on cars.In this case, it's probably a difference in city planning that enables it to happen in Europe as opposed to America.