Who wants to drop a barbell on the back of their neck?
There is a chance you could drop your weights doing any exercise, so why up the risk or ingury. If there is no chance of you dropping it, then your not using enough weight.
The easy answer is that you should be doing presses with dumbbells anyway.
Dumbells give a much better range of motion as you can lower the weight all the way down to your shoulders, and you can drop the weights quickly if you fail.
Unless you are lifting for sport you dont need the barbell, and if you do lift for sport then you would do it in front of the face.