You wouldn't stay there no matter what you do. Like any evasion your opponent will just adjust eventually and attack you in your new position with whatever weapons he can hit you with. In MT that means knees which are readily accessible and he can clinch your head easily and head kicks become very easy to fire.
Ducking down is the legit way you are supposed to throw a straight to the body anyway except you often see people throw a lazy version which they don't get low enough and end up throwing it down at an angle. Trying to throw successive head punches from that position would be awkward as hell and quickly tire your legs out. Try it for yourself. See how long you can stay down there before your legs seize up.
Interviewer: 'He's (Dirrell) a good boxer'
Arthur Abraham: 'No. He's a good actor'