First off the hop, this isn't an argument against the hip thrust because I don't have a real fundamental problem with it.
But when we cue the chin to drive forward and down in the thrust we are really creating a big misunderstanding of what is really happening.
Your chin isn't connected to your GLUTES, it's connected to your cervical spine which runs down to the lumbar spine, transitioning into the pelvis and hips.
Do yourself one favour right now.
Sit down in a chair, and exhale to pull your ribs down - drive your chin forward, then drop it down to your chest a few times.
What did you feel? Did you posteriorly rotate more? Did your glutes suddenly come alive? Unlikely, though it's the same relative position as you've been taught with your hip thrust.
What you likely DID feel is an increase in neural tension as you lengthened and shortened a series of nerves.
While this can easily be mistaken for an increased contraction, it really just represents an increase in perceived tension - it isn't necessarily damaging, but it certainly isn't helping you squeeze your glutes more.
It's just letting your body know that you've reached the end of your rope in a particular position.
Or posteriorly rotate for that matter, though how much posterior rotation you even need is probably pretty minimal.
If you want to pull your ribs down, your easiest strategy is..... To breathe out. Exhale.
Driving the chin forward and down doesn't shift the ribs, it just shifts your head.
Pulling the ribs forcefully down while breathing into the belly and shifting the head forward does what? You guessed it. Jacks up a mountain of neural tension, with no significant effect on the muscle.
Your hip thrust would be a lot better served by learning how to exhale powerfully and expand posteriorly into the ribs than jamming your head forward in the hope you feel your glutes more.
Redirect your effort to somewhere it'll be better used.