1. Ask yourself whether you are complaining about the unsecured closet because the FA refused you a drink when you asked for it (I'm presuming that when the FA didn't offer, that OP pressed the call button and asked for one).
2. Ask yourself what you did in the moment. The unsecured door was a risk to you and to other pax. That's why AA's safety & security policies and thus FAA rules, require that the door be secured. If it concerned you, People who help to solve problems are what make the world go round. If you are just doing this to spite the FA, it's, well---- spiteful.
If having thought about the above, it seems worth it, file with FAA. FAA will send a routine inquiry to AA which will, at a minimum tell the FA about it and that will help the FA and others think more of this in the future.