i think ariel isn't a princess of heart because she just isn't. So what if she's a princess? Being a princess and a princess of heart are two different things. I'm not sure if Alice is a princess, but in the end of Alice and Wonderland, she was leaving with her sister, and in the background was a castle, so maybe she is one. But maybe reason why ariel isn't a princess of heart is because if she was one, she wouldn't have been able to team up with sora and co. since she would've probably gotten captured and stuff.