Yeah, the logic of ths story has me frequently rolling my eyes. "Head armor" that leaves the top of his head exposed? Hell, I could excuse the entirety of his face, since there were historical open-faced helmets, but at this point, it's a glorified bandana.
Actually... Those things have their purpose, and they actually work against inadverted grazes and light blows.
You usually use them with a hardened leather or iron skullcap/hat though, to have that little bit of extra security against grazes.
And no, it wouldn't work against a full-force blow to the head. Nor would an actual helmet.
Concussive force, aptly named.... And if your brain doesn't get scrambled, don't forget most people do not have the neck muscles of a F1 driver and
will sprain their neck
at least when receiving a full force blow against even a proper helmet if the padding isn't the proper type...
In that sense the waifu-not-waifu he's staying at is right: If you let the enemy have at your head, you're fucked anyway.
It's about as effective as a chainmail coif over padding when it comes to protecting you from combat head trauma, and weighs
far less and is cheaper.
When it comes to the eternal efficiency/mobility/protection conundrum regarding armor, it's not a bad choice for a low-budget situation like the MC is in.
Where the author/mangaka
really goofed up is the shield.... It's a glorified buckler, completely unsuited for the type of armour and weapons the MC uses.
To be effective he'd need a heater or medium kite shield. The little dish he uses is next to useless against the opponent's weapons that have been shown, unless you're
really well trained. Which our MC isn't.....
I chalk that one up to the fantasy/gaming trope of "big shield = tank", which is quite...... silly...