Why can't we grow beards?

Going to the original question with beards, I would say its because nothing else you listed above hinders an individual from wearing a gas mask or other forms of masks. A beard would hinder the wearing of these masks .

Clean shaven looks professional. Have you noticed what people look like after they leave the military lately? They certainly don't have 'white-collar' positions.

Spc Cody Voye;
It seems there are those that want to buck the standards for uniform wear to wear beards based on other country’s standards.. “because they allow it”.
The U.S. has it’s standards and those other countries have theirs. We are Not them and they are NOT us.. enough said.!

Well Specialist, let me address this point by point.
The Army has always allowed people with tattoos (some motifs are not allowed) to enlist. You sign a contract and they "own" you as you are, tats and all. However, there is a little used, seldom enforced regulation that keeps you from getting more tattoos while your contract is still valid; it is covered under the defacement of government property, which you technically are. This little piece of AR can also be brought to bear should you get a sunburn bad enough to keep you from being able to wear your uniform.
People with criminal histories, past drug/alcohol abuse problems, overweight issues have, for the most part, been able to get waivers for enlistment but have always been "encouraged" to do their best to conform to Army regulations or risk being put out for non-conformity.
The "psychotic" people you mention is a relatively new thing but I am sure there are or will be waivers available for this as well, within certain limitations. People with chronic health issues that require a regular medication are often not allowed to enlist, i.e, epilepsy, diabetes and the like.
And face it, after you spend time being on the wrong end of some dune-coon's AK, or have been fortunate enough to arrange a few meeting with Allah for those poor bastards, are not we all a bit 'psychotic'?
You need not worry about what our allies do in regards to their military. You are not in their military, so the comparison is irrelevant.
Last I checked, US Army hairstyle regulations was covered under AR 670-1. If you are seeing soldiers with hair not conforming to that reg, then you are obligated to make an on the spot correction, regardless of their rank. Except for Generals, they can get away with that shit.
What do you mean "We have different uniforms"? The Us Army has its uniforms (duty, dress) and they have their authorized variations. Again, if you see someone not in compliance to the regs you are obligated to make the correction (see The General's Exception).

I think the issue returns back to the issue of uniform apperance. If beards are allowed to be a matter of choice, there will always be the guy who has no business growing one. His appearance will just be one step above homeless. In addition, after a epic weekend, I don't have the energy to shave for Monday's formation. The obivious answer is I'm starting a beard. I will change my mind about Thursday. A clean shave equalizes the peach-fuzz and Brillo face military members, including the females.

if it hasn't changed since I retired - what you are authorized to wear off-duty is a dress code from the 1950s
Early in WWi uncle Adolf had a full handlebar moustache which he trimmed to its infamous shape for the gas mask.
The whole military short hair thing was all about lice - in all of world history (includes the Bible) Warriors never cut their hair - who had short hair?? - Slaves!
Had a CSM once who had decided that paratroopers didn't have moustaches - took standards to the extreme, my Plt SGT who never wore a moustache before was one of the lucky guys who could do a pencil-thin-moustach and so wore it the whole time that CSM was there

The answer to your question is, of course, "Murica!"

Everyone knows the rules either follow them or don’t join. Stop trying to change thing the military. To much has already changed and the military is going soft. The military is about discipline

What army are you serving in? Yes there may be waivers for certain things but criminal history, alcohol abuse, overweight, and psychotic people are absolutely not allowed entry into the service. The reason why full beards were stopped was because way back in the day when they were allowed, the was no real hygiene in the French trenches of ww1 and one of the things that spread was Lyme disease from fleas getting into the beards. That’s why it is limited to a mustache. Harder for a flea to live in a mustache than it is to live in cheek stubble.

Well SPC Voye, up until the mid 70's Navy enlisted were allowed to wear beards as part of their tradition. And apparently there was an issue with the seal on the protective masks at the time. Tell ya what, figure out a way to get a shaving profile, grow a beard, then do PT conditioning drills 1 thru 6 in a CS chamber. If you get the faintest whiff of CS you are dead if it was a nerve agent. Then you might understand why we do not wear beards. Or are you wanting to imitate being a Green Beret or a Delta Operator?