You have to do this with subway construction anyways, because New York ended up boring relatively close to the surface. If you're boring twenty or thirty feet (eight to ten meters) down you're still in the danger zone of misplaced utilities.

Going deeper is possible but does have drawbacks; access shafts must be deeper and it takes a longer time for people to move between platform and street level. New York's older cut-and-cover sections also do not deal with ventilation systems, because regularly installed grates to the surface essentially use the piston effect to circulate air in and out of the system.