Cross-draw holsters serve some people very well. Those who spend a lot of time seated or driving gain some accessibility with cross-draw. Some folks with range-of-motion issues in the hand, wrist, arm, or shoulder can benefit from a cross-draw rig.
For most applications the cross-draw has some fairly serious limitations. The reverse cant (muzzle forward, grip-frame to the rear) is less effective at disguising the handgun's outline, and the grip-frame usually projects outward from the body to some degree. These factors make the cross-draw generally less concealable than a strong-side rig. More attention to cover garments is required to maintain reasonable concealment.
From a defensive tactical perspective we are less able to effectively draw the handgun from a cross-draw holster, an aggressor at close quarters can more easily block the hand and arm during the draw, and the simple act of reaching for the handgun can telegraph intent to an opponent. Also, the muzzle of the weapon must be rotated nearly 180 degrees, passing over anything and anyone within a wide arc, before it can be directed at the intended target. At close range it can be easier for an opponent to disarm someone using a cross-draw rig than with a strong-side carry.
Like everything else in holster design there are always compromises among the 4 basic factors of comfort, accessibility, security, and concealability. Only the individual can decide which factors are most important for his needs and how much compromise can be accepted in the other factors.