I think it's like morfiend says, more survivors from hits but more injuries. The British Brodie soup plate shaped helmet was designed to protect men while in the trenches from airburst shrapnel shells. I wouldn't believe the helmet led to more risk taking. Men would be killed daily, helmet or no helmet. Any illusion that the helmet made you immune to that would soon be dispelled. The same argument is also used about any safety device, airbags, motorcycle helmets etc. Never bought into that myself.
I actually own a British WW1 helmet. It's a heavy uncomfortable thing. I wore the WW2 version in my time as a reservist. It was not much better.
As for the straps, they soon become uncomfortable on the chin, so we either wore them open or worn on the back of the head. Part of the reason you see a lot of GIs in WW2 with open straps was the idea than an enemy would come from behind and strangle you with the strap or that a nearby explosion would break you neck. Patton didn't buy into that and in his 3rd Army he had strict rules about wearing of helmets. Later versions of the M1 had straps that were designed to open at a certain pressure.