First they didn’t look like helmets but rather just globes on people’s heads, but I chalk that up to artistic style.
But they were red on top white on bottom with a giant officers rank symbol in the dead center of it, they don’t look like any US military officers helmets I’ve ever seen. Also they’d wear them at all times and not just in the field.
The rank symbols were very big so their rank was clearly identifiable to the reader. If they were actual size, it would be impossible to tell.
Pvt Bailey himself wears his helmet like that.
Mort Walker was a Army vet, serving in WW2.
Regulation Comics Military dress code.
Who makes these rules?
I suspect that it was all a matter of (a) legibility in a tiny piece of art, and (b) making it easy for the reader to quickly differentiate between the characters, because they were nearly all wearing essentially the same thing from the neck down.
Generally speaking, all of the Army characters in the strip wore their headwear nearly all the time, likely again for the reader to easily recognize each character.
Also, just for reference, this is the helmet/art in question:
Lt. Flap is smuggling a poké ball.
Right, OP. Because in Beetle Bailey, it’s the inaccuracy of the helmets that bother you. Not the dog with a sergeant’s uniform or like that. 
Obligatory mention that Beetle is the brother to Lois of Hi and Lois, another strip that Walker drew, that was actually a spin-off from Beetle Bailey.
I’ve seen Army helmets painted like that and polished to a high shine. They were gussied up for parade purposes. Where, when, and how often, I can’t say. But they definitely wouldn’t be used in the field.
Glad someone brought this up. Obviously the graphic style of “Beetle Bailey” is very cartoony but the chamber pot-like helmets they wear and the red and white stripes on the officers’ hats have always stood out to me.
Also how Sgt. Snorkel’s wedge cap has those two folds that stick out like ears and turn downward and then the dent in the middle whereas Corp. Yo’s wedge cap only has the “ears” and they turn upward. When one acquires some knowledge of World War II- and Cold War-era US military uniforms, one can figure out what these weird hat shapes were derived from, but it’s still funny.
I figure the colored helmets were helmet liners. The old M1 helmets had liners that could be worn separately. Different units could have them painted for garrison use.
The “tin hat” worn by British and American troops in WWI (and beyond) was designed to protect soldiers in the trenches against artillery shells bursting overhead. Artillery claimed more victims during the war than any other means of killing.
Before the helmets were introduced, British troops wore cloth caps with visors. The number of wounded rose dramatically afterwards, leading those in command to conclude that helmets were of no use. What they failed to consider was that the number of fatalities fell substantially, a classic case of misinterpretation.
American troops called the helmet that replaced the M1 in the 1980s “the Fritz” because it resembled the German Stahlhelm first used in 1915. The design was intended to provide additional protection to the wearer’s head and neck.
It seems to me that the “Integrated Combat System” used nowadays doesn’t protect anything but the cranium. I wouldn’t want to wear one in a firefight.
Best as I can tell, modern 'tactical" helmets are more tightly fitted, but provide basically the same amount of protection - except for the fact that the ears are more exposed, which is something soldiers generally prefer (either for better situational awareness, or for wearing earphones).
What really bothers me about these odd helmets is that I’ve been reading Beetle Bailey since I was a wee kid (and I still keep up with it via The Comics Curmudgeon).
I knew the hats and helmets were weird-looking BUT NEVER ASKED WHY.
Y’know what? I’m going to put that on my “Research This As Soon As I Retire” list.
(I retired five years ago, and have never even looked at my list…)
The Sad Sack’s weren’t much better:
