It is the longer the hair the more freedom of the bait to go into the mouth.
A short hair won't allow the bait the freedom to be sucked in, so the hook doesn't even go into the mouth.
If the hair is long enough the hook will follow it into the mouth, then with that hook following the carp 'realises' a foreign object is attached or the bait has something with it it shouldn't, so attempts to blow that foreign object out, giving the chance for the hook to pr ick into the lip.
The hair needs to be long enough for the hook to be taken in in the first place.
You have actually picked up on another point
.If they are feeding on close together particles, pellets or groundbait, then you can get away with a shorter hair, whereas boilies that are further apart you will likely need the hair to be longer.
You can actually watch fish in tanks or ponds, if you put a baited hook in there, after a few hookings, the carp will suck the bait from further away, so lengthen the hair and you can continue to hook them.
Now imagine that in a big lake, big as in fishable size, and you can see how the hair needs to be changed to suit.
Rod Hutchinson wrote about most of this in The Carp Strikes Back, so it's not new
Carp don't suck in with the same force each time; each food reacts differently, size, density and the lakebed will change how much pressure to move it is required. Sweetcorn is a light bait, so will require less suck than an 18mm boilie. That 18mm boilie on a firm sand or clay lakebed will need less suck than an 18mm boilie sat in silt. Other particles, hemp or tares are pretty dense and 'heavy', or larger particles like chick peas, maple peas or maize are almost boilie size.
Steve then picks up another point, carp feed differently. Some carp are suckers and blowers, others pick certain foods up, and some truffle, trough or dig the lakebed, especially when feeding on bloodworm or maggots in silt. (Deeper areas that have been cleaned down).
A pop-up rig will need to be considered as to whether the carp is clamping down on it, or sucking the bait in from a distance.