Going without identifying markings isn’t anything new. OSI & special forces operate like that all the time already. Every single military member is going to have a CAC card and generally you’d be integrated with some unit. Outsiders stick out because no one seems to interact with them or know them. Military members are trained to identify and call out people that don’t belong. In the air force the saying used is “every airman is a sensor”. Basically, civilians, even if wearing the uniform correctly (hard to do) stick out because their mannerisms are all wrong. The way you put away/put on your cover (hat) looks weird if you haven’t done it thousands of times.

Active military members are accounted for. You can’t just “pop off to the Mexican border real quick”.

I just don’t really see the scenario that you’re trying to insinuate.

If someone’s got all that, then they’re active military members. Also, the squadron would instantly recognize you as a new face and you’d suddenly become the center of attention within minutes. Even if you have a convincing story, everyone wants to know where you sit in the chain of command. Hell, the way civilians stand would make you stick out.