Building downwards into space that has no natural light makes for housing that is unpleasant and in many cases dangerous in case of fire (on the 1st to 4th stories, roughly; windows provide a secondary means of egress; and above that, fire escapes).

Additionally, building downwards is extremely impractical where downwards is below the water table, which is the case in many parts of most major cities (since cities tend to have historically developed along rivers or shoreline for access to drinking water and transportation).