that is way I say chin back - keeping the head cervical spine as close to neutral alignment as possible while also meeting fighting requirements. The closer one is to neutral spinal alignment the stronger and faster the body will function... that said you can't stand completely in this position while trying to fight.

Now you seem to me to be talking about lateral movement...
My opinion is you keep the center of balance as much as possible pretty much all the time and the head, in my world of teaching, training and fighting, remains 'motionless'. I have my guys practice looking in the mirror with there head lined up on a crack in the wall or something and they learn to do pretty much everything without head movement.

Then they move head when they want, not automatically cause punching... if you maintain center of balance and use core I think this works fine. It also leaves you neutral to do anything after anything...

example - Mike Tyson - bobbing with punches... gets huge power and sets up but is very limited in what he can throw next.

MuayThai, being much much more multidimentional (I would not recommend much lateral head movement - what I do with guys like that is jab and kick - they often slip right into kick - i don't even have to know if they will or not it will eventually happen) anyway... MuayThai and MMA i like the idea of after a right punch one can sprawl or right punch or kick or block or move or shoot of left punch etc etc etc

Keeping centered does this and plenty of power can be generated using core imo