I mean...and here's a bad example, Elsa's a PoH and as far as I'm concerned, and her actions almost caused her whole kingdom to freeze, and her sister to die. I'm not saying that it's worse than Ariel, but...it just strikes me odd that Elsa, the one who's got darkness in her heart, is a PoH and Ariel isn't. I'm not even sure what you listed is really darkness in her heart...
It's just the case that Ariel's an idiot. Also bad examples, but she's kinda like in Riku, Belle, Rap, and Jasmine's place and she just wants freedom outside of her secluded underwater prison, and freedom from her father dictating what to do and where to go. All so he can protect her? Yes, those are Triton's goals, but it's clear that Ariel's the more rebellious Princess...and also she's an idiot.
Out of all the Disney Princesses, there's no denying that her ways to achieve freedom is...VERY questionable and idiotic, but it's clear she has that...freedom-like intention that most of the Princesses have.