Considering the stalemate/static nature of trench warfare wouldn't some kind of body armor have made sense? As I understand it the armor of tanks played an important role in breaking the lines- was the idea of armoring troops just too out of date?
Chain mail will not stop bullets. Chain mail will not stop a direct bayonet spear, only a glance/slice. As for metal body armor, it takes a very thick plate to stop a bullet and would be cumbersome for storming trenches. This along with the materials needed for the number of troops being thrown into battle is not cost effective.
The War Museum in London has examples of body armour used during WW1. The problem with it was the weight and clumsiness of it. It needed to be very thick to work and that made it heavy so it was really only used in stationary positions. This was plate. Chainmail on the other hand doesn't have the same stopping power, though paired with a good gambeson may offer some protection from shrapnel (just by dint of slowing it down). Here we enter into a cost/effect situation. It takes time and a lot of effort to make chainmail and it can't easily be automated. Each ring needs to be riveted closed and it's still done by hand. That and the amount of metal needed just weren't worth the small amount of protection that it could provide (and only in paired with a gambeson).