"If we have artificial gravity on a ship(Enterprise style), would't we have the ability to create other gravity based technologies like folding space for distant travel?"
Simply, the energy requirements would not scale. One way to prevent in universe abuse is to increase the energy requirements with mass and distance and have it in an exponential fashion. You could store and release energy in a instant to jump, but artificial gravity would require power, over a long time. attracting say, a 300 kg creature to a nearby floor mounted gravity generator would be 'cheap'. Heck, you could use it to move cargo. As weight increases, power requirements increase, making gravity manipulation for permanent inter-spatial folds in space difficult.
A 'jump drive' may work in this fashion since it pinches space for a infinitesimally short period of time. However a snap-back effect might happen, with the potential of massive energy release or other side effects, depending on your universe