A downside of synthetic turf is how it retains heat on hot days and standing on the turf can be more than 20 degrees hotter than the surrounding areas. Such a public square would not be tolerable during much of the summer.
I would question whether or not the design concept in a “public square” situation could be successful by substituting synthetic for real turf. The heat, the little rubber pellets, possible vandalism, imbedded animal waste and chewing gum would al be detriments to the enjoyment of the space. Synthetic turf makes a lot of sense for park and school district athletic fields where there’s high turf wear but not enough $$$ to do adequate maintenance. But there are many squares around the world that are done with interesting paving and even crushed granite on a larger scale, then complemented and humanized by trees and planting beds.
And as an editorial note, I find sythetic turfs’ bright green color during the gray, brown winter to be too unnatural for my own tastes..
There are ENDLESS uses for synthetic turfs, depending on the situation. Dog parks, spaces for people allergic to grass, fully shaded areas, sportsfields in low-income areas, daycare centers, indoor public spaces, indoor private spaces, indoor semi-private spaces, bookcovers, on top of roofs, on top of cars, on top of lawns, ok maybe not endless.