A headshot is only quick and painless if it destroys the brainstem. That is a relatively small target that is easily missed. (And hollow-point bullets don't make the task any easier because the brainstem is not surrounded by enough tissue to make an incoming hollow-point bullet expand significantly.)

If the brainstem is missed...

Without the frontal lobes the brain can still survive; ask Phineas Gage.
Without the upper respiratory tract, there is the risk that the body (and brain) can still survive via artificial life support if the EMTs' attention is drawn too quickly.