also, spoilers for 273 are out, I'm starting a new thread for it.
The term "princess" is actually somewhat disrespectful, in the way Harima uses it. If he wanted to give Eri special treatment, he'd use the term "ojou-sama". I think the difference is that where most people see Eri as some sort of elite figure, Harima sees her as a girl with strengths and weaknesses. That's why Eri doesn't have to try to live up to any sort of image around him; she can just be herself.