The (European) city I live close to has done this very step about 30 years ago when their main shopping strip was converted to a pedestrian / bike-only street.

However, everytime I go there, the street is still full with cars: delivery trucks that bring the retail goods to the stores (which are not easily accessible otherwise), construction trucks for the apparently constant repairs they're doing on the road, ambulances, etc. Even when most of them are not driving you're still constantly surrounded by (mostly big) vehicles.