OP said nothing about a "drop ceiling". they suggested a drywall ceiling.
Doesn't matter; on HGTV they rip those out too. (Usually the house in question is an old Victorian or Craftsman and the ceilings were lowered in the '70s or something.)
IMO, the key realization is that houses are designed on purpose. The high ceilings in old Victorians served an important function: namely, keeping the place cool in the summer without A/C. The low ceilings in mid-century ranches also served an important function: namely, keeping the place cool in the summer
with A/C, without having to run it excessively. If you're thinking of changing something like ceiling height in a house, you have to first understand how it was designed to work as a system, and then decide whether you're willing to properly
re-engineer it to continue to work well as a system.
Making piecemeal changes is a way to really screw up the house (one good example is adding insulation to a house that didn't originally have any -- without adding a vapor barrier too, it can suddenly start molding or rotting).