Well, she's not going to play any political role because she was only just born. It'll take a few years (or moons) before she's ready for any taxing responsibilities like those that the other alicorns have. Sure, she might be created by Hasbro for more merchandise, but DHX executed her introduction incredibly well in my eyes. But I do agree that debating what type of princess she is is pointless, since it's obvious that as of now she doesn't hold any political power, thus making her one that's considered a one purely by royalty. In a sense, picture of a king and queen in our world had a child. That child wouldn't have any political power from young, but they'd still be a princess. Eventually they get older and can play a role in their land's politics. It's the same thing in Equestria, just with princess and prince being more general terms.
Also, alicorns being born isn't against the shows canon. It wasn't once stated throughout the show that alicorns couldn't be born, as we haven't ever really gotten any backstory on them prior to this, save for the fact that the S3 finale revealed that ponies can be turned to alicorns. I could understand the confusion about how people thought that doing something of great worth is the only way to achieve this title, however the S6 premiere revealed that there's now a second way. Besides, it would make sense for alicorns to be born, as we haven't seen any other alicorn in a stable (no pun intended) relationship that could lead to a baby being conceived, save for Cadance and Shining Armor being in one. The 'alicornisation' process would likely alter the genetics of the pony who achieves it.
But I understand your point. We don't really know what they have planned with Flurry Hearts, and speculating on what they may do is pointless, since there really aren't any clues to lead us towards any solid conclusion. As you said, we should just wait to see how things turn out.