Had to go to NYC briefly and randomly encountered their "making Park Avenue free of cars" day. I'd guess more cyclists and pedestrians traveled on it than people to do normally in cars (I'd guess a lot more, actually, but don't know if I am good at estimating such things) and the city didn't grind to a halt.
You don't have to close all the streets to cars all the time, but pretty sure you could randomly close 5% of them and improve life immensely. Give it a bit more thought and even better.