*Yes, I know some princesses don't fit these requirements, but they are often said not to deserve to be in the line-up, and for reasons included in the poll. You can take that into account or ignore it when you chose.*
I don't think this really affects the character very much. It does affect marketability to an extent, but I think the others do so more. And I'm not picking Princess by birth or marriage because I think the princess should be a princess OR the protagonist of her movie. But just my two cents.

People need to consider that just because they think that each princess should sing one song (I do too), does not mean that it is important factor in the COMPANY's decision. A lot of people are choosing what THEY feel is important without considering it through the COMPANY's point of view, so practically choosing to see what they WANT to see and not an overall importance.

This does not really matter much, since the princess formula is changing more and more (with less films being a musical), and this does not determine a reason why a character gets to be a DP. It just has little to no impact. Now that Merida is included, a lot of prior rules do not count, and you can't ignore it because it is only one character.

Take Sleeping Beauty, on the list of how much money each movie made it in the 45-50 and we still have her in the in lineup.

Or Film successful at the box office.

Mulan isn't a princes by birth or marriage, and she's in the line-up.

I don't really care whether or not she's royalty, nor do I care whether she married royalty.