Of course there are some problems with putting the road system under ground.
Higher construction costs
Putting a roof over all roads will of course cost more in construction costs, but on the other hand land usage costs will go down. As a city becomes more dense, with higher buildings, the cost of putting the roads under ground will go down per housing unit.
Higher maintenance costs
Maintenances of underground roads is higher than roads up in the day, a cost which ought to be greatly compensated for by the time savings citizens will enjoy due to shorter travel times.
An Ultra Compact City will be a bit like one big building, and tearing houses down will be more difficult than in a traditional city. Consequently care must be taken to design buildings such that they both can be removed individually and to ensure buildings can be upgraded or their usage changed throughout their lifespan. Generally, the skeleton of the buildings should be built to last the centuries, while the rooms and internal layout should be changeable.
High levels of pollutants inside tunnels
Pollutants will not easily escape from an underground road, something which is great for people outside the tunnels but a problem inside. Air filters can be used in cars, dust particles can be cleansed from the air, and air must be ventilated out and released away from street level above, but there will be more pollutants inside the tunnels than on an outside road.
High noise levels inside tunnels
Roofs and walls will reflect noise back on the cars, giving higher noise levels than before. This can be reduced with noise dampening materials, but this is more expensive than naked concrete. The upside of this is that noise is removed from the topside streets and pedestrians that don’t have a metal box around them to dampen the noise.
Boring views for drivers
It is probably smart to open up the tunnels here and there to give drivers some daylight and a chance to catch their bearings, but it will obviously be pretty boring to drive around for a few hours under ground. Hopefully drivers will find that shorter distances and less queues will make up for it! Also, keep in mind that within a decade or two it is likely we’ll be sitting in the back seat watching TV or surfing the web while the car is driving itself.
Automotive transport isn’t eliminated
Sorry. I don’t see how a modern city without point-to-point automotive transport will work.