It's a bit of a shame there's no helmets for beast races. I'm playing an Argonian (yes, peer pressure forced me to get Steam >.>) and of course I can't wear a helmet as I couldn't logically explain where my horns would go if I wore one. So... I don't.
But for all other races and as far as logic is concerned: The helmet is the most important piece of armour. NO sane warrior would fight without a helmet. For most medieval fighters, the helmet would be the only piece of metal (except for the bit at the end of their weapons) they'd equip for battle. Much less expensive than a full suit of maille (or, in very late periods, plate, but that wasn't commonly around until the very late medieval times). The thing is, the head is the most vulnerable part of the body, and easy to hit in melee. It's what you need to protect FIRST before thinking about chest armour or anything. Only protecting the chest is a very recent invention that came with modern firearms; the torso is simply the largest target, most shooters these days are trained to aim for the center of mass, so yes, police usually only wear ballistic armour to protect the chest. But this isn't a modern scenario, melee threats are common, and the head needs to be protected (don't forget that even today, soldiers always carry a helmet, while their body armour isn't always the best, depending on the deployment zone and nation of origin, of course; but if you can, the first piece of equipment you'd get, as a fighter, now and back in the middle ages, was a helmet... Well, after the weapon, that is).
So yes, not wearing a helmet should come with massive disadvantages in combat. It should be stupid. Only true problem is, as I said, beast races who'd need helmets that work for them.
That enlarged sentence is incorrect; the briastplate was the most important piece of a Greek hoplite's armor 2500 years ago. Yeah, the head's a vulnerable point, but it's a small target and people tend to move it out the way of a blow pretty quickly. If I were fighting with hand-to-hand weapons and had the choice of a briastplate or helmet, but not both, I'd certainly take the briastplate over a helmet.