Underground Skyscrapers

Instead of building the world’s tallest skyscraper, why can’t we start building the world’s deepest building?Edit
Instead of building skyscrapers up, why can’t we build them down?
In cities, buildings could be built below the pipes and the subways while there would be some saved space above
for other recreational and residential buildings.
We could stop worrying about skyscrapers being targets of terrorism and weathered building materials.
I am not an engineer, so therefore I’m looking for what everyone has to say about this (engineer/architect insight
preferred but not necessary) on the benefits and problems this may have on society, the environment, life of a building.
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