If the author was a little less dumb about this entire plotline to "test" Akira, I would probably resent the princess a little less. In the first place, not believing that he had actually injured his mana veins or whatever and then having the wizard girl refuse to cure him is just sad. Dragging him into danger when he's basically crippled just to make sure he isn't hiding his talent from them. Heisei manga are all like this, the protagonist has no real agency, the people around him are all unreasonable to force them to do things that are convenient for the plot, and characters constantly make mistakes that are convenient for the plot. That's why so many people enjoy true Narou-kei works.
I'm hoping he will get at least one heroine who is genuinely honest with him and loyal to him, like maybe Prol.