Construction workers don't just wear them for reassurance either.

They protect the most vulnerable part of your body. You might not immediately go tell tales of it if you get hit in your helmet by anything but a small caliber or shrapnel (a large caliber will still inflict significant head trauma), but your chances of survival are way up from pretty much zero.

Also there might be all kinds of stuff flying around on a battlefield, and even if it isn't necessarily lethal, it's nice to not get hit in the head by a rock or whatever.

In the first world war they apparently shielded the wearer effectively from debris caused by artillery shells that would have otherwise killed them. Here's an interesting video about the statistics behind it (and how they were misinterpreted at first): https://www.youtube.com/watch?v=1IQE0uZUMys

They probably aren't that effective at stopping bullets coming straight on, but they will protect against ricochets, shrapnel, falling debris, and so on.

WW1 helmets are as effective as their modern day counterparts

https://scitechdaily.com/shocking-results-when-wwi-helmets-w...

Soviet tank crew wore padded helmets inside their tanks to protect their heads from impacts with the sides and equipment, e.g. while crossing rough terrain or from ill-considered sudden movement

There is a good reason the US changed the bottom profile on its combat helmets, despite any possible associations with the Stahlhelm M35.

They can deflect bullets depending on the angle at which they come. They'll definitely stop some shrapnel and rocks falling after explosions.

And remember that injured soldiers are as much if not more of a problem than dead soldiers because now you need someone to take care of them.