This is going to get unwieldy, but I want to respond point by point:
MOOIOO
Most buildings on military installations are not necessarily access-controlled unless they have a specific reason to be. You've already controlled access to the base by only allowing people to enter with proper credentials or background checks. She would not need her ID in most cases unless she left post and needed to come back on.
He was a small arms maintainer. He likely had unaccompanied access to the arms room, which requires a background check and the commander to approve. No key is necessary to open the main door, and if the cage door was shut, he likely had a key assigned to him permanently. The only odd thing that would become apparent at some point is if someone checked the alarm system logs and saw that he came in and disabled the alarm at 2030, but that was unlikely to happen until a physical security inspection.
This was during the self-isolation period of COVID on Ft. Hood. Most soldiers were confined to their barracks during this; there would not be a lot of people out and about doing things. She was out because she needed to complete an inventory.
I'm not sure why you think no one was looking for her - just because they didn't start a massive formal CID investigation in the first few hours she was missing doesn't mean people weren't actually out there trying to figure out where she's at. If an adult you knew didn't show up to an appointment and you can't get in touch with them for a few hours and called the police... What would the police normally do? Do they immediately start an all-hands search for someone missing for a few hours?
I'm not sure what impression you have of military bases. There aren't roving guards throughout all buildings all the time. There are MPs that respond to alarm signals and emergency calls and patrol the post in general. That's about it. It's not prison...
These are gross mischaracterizations. Do you have guards roving throughout the halls of your workplaces at all times? Oppressive presence of force that sees everything all the time? I'm also not sure why you say "no one bats an eyelid". People were looking for her, locally. They were trying to figure out what happened. It's easy to say after the fact, "You should have known she was murdered!" but realistically, how likely is that? After several hours passed (less than 24), and they could not find her, they immediately reported it to CID and an investigation and full search was started. That's incredibly more than you'd normally get in the civilian world.
Didn't think it was relevant, or thought it would be silly to report until it bothered them enough to report it "just in case". (MOO)
It's possible her arms room did not have a storage rack for the .50cal weapons being referenced, so they were stored in AR's arms room. This is common. It appears he worked in the headquarters company/troop for the battalion/squadron, so this would be a common arrangement. Her being in her headquarters' arms room isn't weird or suspicious on its face.
Not trying to be rude, but it doesn't make sense to you because it appears you're unaware of or have little experience with daily life on a military installation. Not much here that you have highlighted is actually strange.
ETA: There is also a weird tone with your post. You act as if soldiers are supposed to be babied or constantly monitored or supervised. They need constant guards, and why aren't supervisors constantly around monitoring them? "Twenty somethings" are just allowed to do whatever they want...
Soldiers have an immense amount of responsibility, and are generally expected to be fairly autonomous. You're cool with handing that same twenty-something a rifle and telling them to go kill bad guys for you (not "you", personally, but "you" in general), but heaven forbid they not have constant supervision in garrison because they're all of a sudden not responsible adults anymore for some reason.
