So, greathelms are actually quite varied as they evolved out of the need to protect the head and face better as cavalry became more significant. While infantry has always been the backbone of armies, during the high middle ages, the cavalry soldiers were essentially the game winning option in most cases, and needed to be well equipped.
The first type we really encounter is the enclosed greathelm.
They follow a pretty simple process, honestly. How do you stop the skull being split, and also prevent a blow to the face instantly ending you? Reinforce the skull, add a faceplate. But the issue here is the back of the head is exposed, the skull is still vulnerable to direct blows, and the neck is also a target. So, you enforce the helmet further.
Okay, now we're getting more protected. The flat top has a high ridge, so blows there are less of an issue. The ears, side of the head, and back of head are covered. But, the flat top does mean blows are going to rock your head around, and the neck is still kind of vulnerable. So you round things, and lower the face further...
Now we're getting somewhere. The neck is mostly covered by the faceplate now, while we have a small top that's less flat and more ovular. Direct hits to the top now slide away better. Visibility is pretty good. Looking up and down is a bit hard, but if you're doing that, are you really cavalry?
Still, we can make this even better. What about making the top more rounded for extra protection, and if the faceplate could move so we can see and breathe better?
Well, that's more like it! Now we have good cover, visibility, and airflow. And the pointed top is kind of stylish. Hey, wait a minute, isn't this...kind of a bascinet...?
Well, whatever works, works. So what if we made the whole helmet absolutely huge, to cover our head and allow us to just eat lances to the face?
At this point, I can wear a smaller, but complete helmet underneath this one. Go ahead, hit me, what the FUCK is a concussion??
But as cool as this is, I think we could make this even more outrageously protective. The visibility isn't quite as good as other options now (such as the bascinet and early sallets), but the protection when in the saddle is incredible. So what if we took this even further?
The frogmouth helmet, specialized for jousting. Visibility is poor when you lean upright, but nothing is getting into our faces. Lances will slide away from our neck. Debris will bounce off harmlessly. This isn't a helmet for mobility and vision, it's for absolute protection.
Essentially, the greathelm goes through a lot of phases, and is constantly improved upon. It's a super cavalry helmet, having some of the best forms of protection, but lowered visibility and often less neck cover (something the great bascinet did better, albeit largely by reinforcing itself akin to a greathelm). The pinnacle is the greathelm is the frogmouth, which gives the absolute best protection for a jouster, though little mobility and visibility, making it exclusive to mounted contests of arms.