Of course it's mainly played off for laughs, and even more disturbingly, Carla thinks that the way the head maid treats her is justified. After being defeated, Carla is loyal to Souma and Licia, not just because of the slave collar, but because of her own convictions. It seems wrong for Souma to be in the process of abolishing slavery in the kingdom, but continuing to keep Carla as a slave and allow her to be mistreated. Of course whenever he needs her help, he drags her out and she loyally protects his life. He rewarded her father with almost no sentence because of his loyalty to the kingdom, how about doing the same for Carla. I think this story is a cut above most Isekai, but the way Carla is treated drags it down from where it could be.