So why would AA have this policy? Why would someone who works at corporate and is traveling on their own time not be allowed to buy a membership with money out of their own pocket?

Shouldn't employees traveling on 100% revenue tickets paid entirely out of their own pocket be treated like any other revenue customer?

Couldn't they just make a rule where employees using the lounge on their own time out of their own pocket be dressed in a way that no one would know they're an AMR employee?