The artificial gravity is a byproduct of the inertial dampeners. You don't mess with the inertial dampeners unless you want the crew the slam into a bulkhead at .999C.

"Why can't we route power from gravitational engines?"

"The show's budget cannae afford such excess, Cap'n"

"What's that, Scotty?"

"The- uh- the dilithium core only works properly in a gravity field, Cap'n. We'd lose more power than we'd save."

"Ah yes, that makes sense"

They could, because grav plating holds a residual charge so they'll be able to maintain gravity for a period of time before people start floating