Well, he doesn't need to, because he's not drawing from the artery at regular intervals, I hope. (Pardon me, but out of curiosity - hemochromatosis?)
The point is that you have two arteries running to your hand, the radial and the ulnar. In healthy people one can take over for the other for a while if someone blocks it with strong pressure or an arterial line (used to measure blood pressure in critically ill patients on pressors, stroke patients with a very specific blood pressure goal, etc).
In people with say vascular disease or variant anatomy, the hand needs both and will die otherwise. So you have to put your line elsewhere.
It probably should be performed before arterial blood draws because it is possible, albeit rare, to really mangle an artery. But hardly anyone does this because usually the one drawing the blood is a panicked, sleep deprived physician in training who is under a lot of pressure to get that blood immediately.