If you listen closely to the background chatter on the first few episodes of ST:TOS, you’ll hear a nerdy sounding guy saying “gravity is down to point 8.” But in general, even in written sf, it is easier and faster to ignore the problem. 2001 is about the only real sf movie that actually cares about this.
Not only does the Falcon leave quickly, but its engines are laughably tiny for its speed. Ditto the shuttlecraft in ST. In fact, artificial gravity - both to give one g under no acceleration and to counteract the massive accelerations all these ships are capable of, must use the same technology as tractor and pressor beams.
I’ve tried to work out a lot of these issues for a book, and decided that lots of little gravity generators in all floors was the only practical solution. However that doesn’t work for the case in point, since unless there is a no gravity zone in the walls (and no one floats in the DS going through a door) why isn’t the structural loading on internal members the same as it would be on earth?
Dealing with the problems of artificial gravity would make an excellent Analog story. Probably a funny one too if you had the characters make a lot of mistakes.