I don't think so. I'm not in US, but here „third place“ was not a thing regardless of density. In fact, now climbing out of ex-soviet past (read poverty and totalitarian regime preventing the third place as well as urban sprawl), we got both urban sprawl and growth of the „third place“. Well, little growth from next-to-none. Which is hitting a low ceiling of rather intraverted culture that is caught up in TV and interwebs. Why go to bars if everybody is sitting in tight groups-of-friends and scrolling together...

Ironically, somewhat-third-place, seems to be most active in suburbs and rural areas. Where neighbours need to work together to solve various community issues. And that turns into partying together as well. It's common to have a community house where everybody can use the space for organising whatever, from playing table games to art classes to random lectures to movie nights. While densier cities seem to be less socializing outside of family&friends circles.