I've read the concerns about "limited field of vision" requiring the performers (or, in universe, the crew) to twist their torsos to see around. Seems to me the Apollo lunar suits had the same issues. The Apollo helmets may have afforded a few more degrees side to side, but not much more. I suspect it's more a condition of "perception". The "visor" of the TW helmets wrap over the crown of the hed and down the back, inadvertently drawing attention to the width. For a humanoid with forward binocular vision, such a feature is useless. My "in universe" rationale, the suits and helmets were "contracted" and the they were originally made by and for a Federation species with eyes possibly in front, on top and on the back of their skulls. But other than having a feature useless for humans, Vulcans, Ciatians, etc., they proved perfectly serviceable.
In the real world, the design is quite clever. An ongoing issue with TV and movie space helmets has been adequate ventilation and/or "fogging". Give the helmet a solid visor and the actor is going to become short of breath and what little he has will obscure his features. Some early productions literally drilled a matrix of small holes in the visor. Others would provide a gaping aperture positioned in line with the performer's mouth. Some movies flat out omitted a visor, hoping the audience would just assume one was there, perfectly clear.
But what was done for "The Tholian Web" was just dang ingenious. Rather than "fight" with a plastic or glass faceplate, a fine wire mesh, similar to "screen door" material was stretched across the helmet. Air flow was all but unobstructed. The mesh could not "fog" and the mesh would not "catch" the stage lights in the same manner and glare it into the camera. Finally, upon 1960s televisions, the mesh looked more like some exotic material, having some irredecent qualities.
Now, they could have constructed the helmets to be "solid" across the back, but I think they were "open" for a couple of reasons. One, even more ventilation for the performers. I'm sure they appreciated that. two, a detail just to be different from the props used in other shows and what was being developed by the real space program. Let's face it, see the TW helmet and no one would mistake it for something used on another TV show or movie.
Again, I think the restricted field of view (well, no worse than other helmet designs, except totally clear "fishbowls") is an illusion caused by the "wrapped over" nature of the visor.