Official AA policy is to not accept a checked bag for a flight after the cutoff time. The system is programmed not to allow this and it can only be overridden by a supervisor based on the circumstances. It's rare to get a bag late checked on AA, as Jason Derulo found out a few weeks ago...
It has nothing to do with positive passenger bag match; it's how AA chooses to conduct their business. They
could mark the bag with a late tag and have the customer sign the release stating that they acknowledge that their bag may not make it, but it may not be worth the headache at the destination when the bag doesn't make it and the customer is fuming despite being advised this was the most likely outcome.
The only form of voluntary separation AA allows is for elites who wish to SDFC to an earlier domestic flight after checking bags.
Agents: I’ve learned that the most I can expect from my team is that they try their best. I don’t blame agents / ramp workers for this policy, but applying a policy without thinking is not trying. There is no practical difference between checking a bag at 45 minutes and checking a bag at 44 minutes. If there’s an education standard for employees in a position, then there’s an expectation that those employees apply some critical thinking in a way that promotes the interest of the company while serving the customer.
AA agrees with you on this: there is a 3-minute buffer built into the system. They don't advertise it and I'm loathe to even mention it because then we start having a discussion about the practical difference between checking a bag at 41 versus 42 minutes.