In my experience BA service is often excellent, and occasionally poor. This sounds to me like you have hit middle ground here. I do understand your frustration in being given machine like responses which would annoy me too. I have never actually complained through CR as such for this very reason,and certainly wouldn't regarding matters whereby BA were just following their own policies (however inflexible they may be). If they had severely broken cast iron promises the case would be different, but for not being more compassionate and discretional would not fit the bill for me.........seems more hassle than it's worth tbh.
It is unfortunate that loyalty doesn't count for much these days; it should do, but rarely does in any walk of life anymore.
Just out of interest what caused the delay? Too late now, but always worth trying to establish at the time. If the delay was say an operational reason that staff could pre-empt well in advance, I personally think AA could have handled the situation differently. However, if everything was running tickety-boo until doors closed, aircraft still on stand due to creeping ATC delays then I feel their actions were wholly correct.