After you've done that, in combination with sidewalks, you have effectively created a pedestrian-only street above the cars.
The cost of that is immense. Why not just make the surface (ground level) street more accessible to pedestrians, and keep the businesses where they would prefer to be?
Every city I've visited that has an extensive skyway system is also a city that gets severe winter weather. The skyway is not so much about protecting pedestrians from cars, and more about protecting them from the weather.
None of the vaguely famous underground/above-ground roads in Chicago, notably Wacker, Congress, and Michigan Ave, are pedestrian only above ground. It would also be pretty much lying to define those three roads as "large parts". There's probably 10-15 miles of drivable underground road in downtown (maybe less), most of which is used as not much more than service roads for garbage pickup and loading docks for the high rises above these.
Chicago is also somewhat of an exceptional city in this regard in that it was to an extent demolished and rebuilt twice, and the city was further built up from water level to accommodate underground plumbing and (IIRC) to reduce the swampiness of the land.
The cost of that is immense. Why not just make the surface (ground level) street more accessible to pedestrians, and keep the businesses where they would prefer to be?