AA needs to pay. First thought is some overly enthusiastic AA security person going way too far in doing the identification that they should be leaving to law enforcement.
There is also the very real possibility of retaliation if I were to attempt to follow up with any sort of complaint process. This is a department that is notoriously infested with gangs. They have sent deputies to threaten a FBI agent, "lost" a FBI informant in their jails for weeks, etc.
Anecdotal evidence hints that that may be part of their training. I was held in line for check-in for checking in in LAS for about 1h, prevented from speaking with somebody at the actual check-in counter, all because I couldn't provide proof on my phone that I had uploaded COVID documents to the VeriFly app (which wouldn't allow me to upload said document because the first leg of the trip back to Europe was through UK which lifted all restrictions). The AA staff person threatened to call security if I tried to move ahead and speak with the check-in counter staff and instead told me to wait until he sorted out things.
After a few exchanges like that where I was in retrospect way too polite and complying, he smiled and told me that I'm stuck there and there is no way I'm going to fly home.
At the end of his shift, the next person was super polite and wanted to help me, but it was too late since the check-in window was closed.
I can only describe this behaviour as sadistic. It seems to me that this person had been told that his job was to make sure order was upheld and he used that as an excuse to exercise power over other people.
You might also consider disputing the charge on your credit card. In the end, you presented yourself for check-in and were unjustifiably barred from the flight through no fault of your own.
I just wanted to share my anecdote for the human angle: some people enjoy exercising power over other people. It's not dissimilar to issues that the police force faces, although I would expect an airline to be better placed at rooting out this kind of bad elements from their workforce.
They are interested in what makes their lives easier, which is to pack people into cells and wait for the notoriously slow justice system to sort things out. There's no consequences for mistakes, so there's no incentive to improve.
It should be shocking to the core that anyone, innocent or guilty, would be subject to these conditions. But police just aren't interested in improving them.
I don't deploy it lightly, but the reason I've come around to ACAB (All Cops Are Bastards) has nothing to do with the personalities of individual officers (many of whom are quite nice people). Instead, it's an acknowledgement that every officer subjects people to this sort of treatment as a matter of course. They cannot avoid treating people inhumanely with the current incentives.
Availability of judges and the staff to move people and so on?
Surely you’ve experienced situations where staffing impacted things…
We can debate small perturbations and shifts in employment, but I am not at all convinced this is the reason for majority of the COVID excuses. Especially for a judicial process where people's employment is pretty much secure and hasn't had that much of an impact. Nurses? Sure. Package delivery? I can give them the benefit of the doubt. I see a disproportional number of things are out of order because of COVID. We can act in good faith for a while, but to me it has started to raise my cynicism.
The police willfully caused it to continue.