It looks identical on both jeeps though

Not reducing more than 1 or 2 lbs doing that (or maybe 5). Still, reducing that kind of weight really isn't going to make much difference-that's within the range of weight difference between two soldiers. 50 lbs? For sure worth it (like the useless windshield).

As little as I think it helped, I'm going with improved air flow for the radiator.

Given the kind of radiators they had (all copper, and damn dense fins), and the minimal fans behind them (directly driven off the water pump, so only ran at perhaps 1/2 engine rpm, meaning practically useless at idle), with no shroud around the fan to improve it's poor performance, I'm guessing any air flow resistance that you remove may help, especially in places like this photo.

Thinking about it, those vertical bars probably created a nice dead zone behind them at certain speeds, since each one would cause a vortex on either side. Would be interesting to see some fluid dynamics of such things (I'm not an engineer, just have one in the family).

It's odd the things that improve performance on old vehicles - sometimes you just never know, since they weren't engineered as extensively as modern vehicles are.

These jeeps are only a few steps removed from factory machine works - they're very simple, using quickly-engineered stuff to achieve a bare minimum (like so much military hardware at the time). It was all kind of "get something, anything modestly functional out there". I doubt there was any functional testing specifically aimed at the grill, probably just "well it didn't overheat during testing", and "look how open it is, how could it be an issue".

Or, as someone else said, it was damaged. Maybe both were - possibly a common issue?

I would guess for increased cooling in a hot climate to prevent engine overheating.