There are some negatives. If you are using the pistol for defense, there are times you would be unable to draw. You reduce the ways you can protect your sidearm. When training, you flag everyone to the right side of you during your draw, making you quite unpopular with the instructor as well as those other students.
It is a method, and people should use according to their needs, but for every time you think a crossdraw is a better method, I can show a weakness to it as well as a way to make it work with a gunside draw vs a cross draw.