TL;DR It's incredibly important your cervical spine, skull, mandible et al. This bone resting further up or down than it should correlates heavily with all sorts of craniofacial and spinal issues. It should be sitting somewhere between your C3 and C4, NOT tucked up into your neck behind the mandible
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As I understand from the article, your hyoid bone shifts in and out of it's correct position as we adjust our head-neck posture. The implication is improper posture (kyphosis) leading to craniofacial and spinal issues as TGW stated earlier, with recommendations that the retrognathion (chin area) not going lower/higher than C3-C4. Often I'll tilt my head down (to give that model look) whenever I walk or talk to someone however I'm now learning this may be - bad! My question to TGW is: Can this information be used beyond injury prevention and aid users who are looking for more aesthetic benefits?
All I saw was proper neck positioning and head alignment but how do we regulate the hyoid position? Any movement that we need to make?
Can you consciously move your hyoid up and down? I'm able to, and I'm sure everyone can with a little bit of effort.
Consciously keep it low while mewing, if it's anything like mine then it will be gently resting just lightly against the thyroid cartilage (Image Attached)

You can see in this image that this cartilage ends exactly at the C3/C4 middle ground discussed earlier. This diagram is actually showing an incorrectly resting Hyoid, but shows how the thyroid cartilage forms a nice little cup for the the hyoid to sit in right where it's supposed to rest! You can probably feel this with your own fingers on your throat if you move the hyoid up and down - it fits snugly into the cartilage area that is built to house it.
Can this information be used beyond injury prevention and aid users who are looking for more aesthetic benefits?
Return to proper muscle postures and strength (all the muscles attached to the hyoid, of the neck and tongue) causes a return to aesthetic bone formation. Pulling that hyoid down while mewing might initially give you a double chin, since you're also pulling tongue muscles down into the throat with it. The philosophy is that poor muscle posture failed to stimulate bone growth to its genetic blueprint: The goal is to epigenetically stimulate the forward growth of the nasomaxillary complex by returning to proper muscle posture. Spine and pelvis/sacrum issues are fixed alongside - it's not done piece by piece, everything gets fixed together.
I only corrected this previously unknown issue three days ago. It's a major posture correction that has been previously overlooked
Does this mean create a double chin look then? Also am I correct in thinking this lowering of the hyoid is supposed to help bring the jaw forward over time by counteracting the upward forces of the tongue?
I'm confused about this... so I noticed when I hard mew the way I do, my submental fat/turkey neck is gone. However, I think I understand this mewing in the throat but... it's difficult and uncomfortable. That said, I don't want to "fraud" and do what looks best now if it doesn't help me down the road. I'd rather look bad for some time and have a better result in the end. But I'm not sure if I'm doing this right. Yes, I get the double chin with pulling my tongue in to my throat and the hyoid bone goes down. It seems to happen just doing a Mackenzie chin tuck as well. So this is a better way to mew?
What influences a more ideally positioned hyoid, just things like proper swallow technique and push swallows...?
Remember this pain... and let it activate you.
This is related to the push-pull mewing I have been trying to illustrate. Pushing the tongue/hyoid structure towards the palate encourages shoulders to rotate forward into a mildly kyphotic posture. Pulling the tongue/hyoid backward encourages the shoulders to rotate backward and chest to expand outward. Both need to exist in balance:

The hyoid must be stabilized between these forces. Neither excessive upward and downward movement are ideal.
I know I am not the only one still confused. Any right and wrong illustrations?