I'm going to disagree with you on this. While the head grab might help him keep his balance and help him get his orientation correct the real reason for the head grab is that this is the signal that tells the hen to raise her tail up out of the way so he can hit the target. If it were not for the head grab there would be no fertile eggs.
@Shadrach you are good at observation. Pay attention when they are mating and I think you'll see that I am right.
@Galaxy_rules I'll copy something that I wrote about mating between consenting adults to explain the "why" behind parts of the mating act. Not all matings go this way, especially between juveniles, but it is sort of the ideal. I'm not sure if yours are adults or not.
It is not unusual for a feather to fall out during mating, either on the back of the head or on the back where his claws are standing. That's generally not a problem as long as so many fall out that the bare skin is showing and can be cut by his beak or claws. If the entire feather falls out it should soon grow back. But if the feather is broken and a bit of the shaft is left behind that feather will not grow back until the hen molts.
Here is that right-up on mating.
Mating Between Consenting Adults
1. The rooster dances to show his intentions. He lowers a wing and sort of sidesteps around the hen.
2. The hen squats. This gets her body on the ground so the rooster's weight goes into the ground through her body instead of just her legs. Most roosters of the same breed as the hen are heavier than the hen so the squat is nature's way of protecting her legs and joints.
3. The rooster hops on and grabs the back of her head. This head grab helps line him up right and helps him keep his balance, but the main purpose is to tell her to raise her tail up out of the way so he can hit the target. Without the head grab he would not be able to get to the target so there would be no fertile eggs.
4. The rooster touches her vent with his. That deposits the sperm. This may take a couple of seconds or may be over in a flash.
5. The rooster hops off, his part is done. The hen stands up, fluffs up her feathers, and shakes. This fluffy shake gets the sperm in a special container where it can stay viable from a week to maybe three weeks.
It doesn't always go this way between adults. Sometimes the rooster does not dance but just grabs and hops on. No harm no foul, but it shows he does not have the self-confidence he should. Sometimes the hen runs away instead of squatting. The rooster may let her go or he may give chase. If he chases the hen may squat, she just wanted to know he was serious. He may stop the chase pretty quickly and let her go. He may chase her down and force her. As long as she squats and is not injured it's all OK. Even when he forces her it is usually not very violent.