This is putting the princess in danger down the line. Likely when Rain will have to choose giving something up, either the princess or something of equal value.
No, this ship will never sail very far. It's a red herring. While her admiration is beautiful and her will strong, she's obviously just using Rain as a substitute for her father. Which she wholeheartedly shows here. Even if a relationship ever-so-slightly blooms, the demon inside the Princess will not allow it. She's full on Yandere.
Side note: You guys, thinking that the princess doesn't understand the world, are wrong in your assumption of her. She understands it pretty well. She probably knew he would leave, which is why she had those thoughts of, "He never said he'd stay with me." Her dream is a future that will come to pass. We're not talking about split timeline theory or anything; it WILL happen. If Rain stays, Rain dies. So she pushed him away, stripped him of the duties that bound him there, so he wouldn't die.