I think the point of the new girl is exactly that, she isnt a member of the harem and i have certainty that she will never be, she is here to cause conflict for good or bad.
Harem stories have the weakness to fall into a slump because generally, the MMC has always the standard shy personality, which isnt really strange for a teenager boy to have (even if many stories exacerbate it a lot), so to avoid this an element of conflict needs to be put in action, generally, it would be just another harem candidate or member but this author knows that this is already to played out so he chose to put a girl that isnt a candidate to shake things up.
So we don't need to like her, because she isnt here to be liked, with that in mind i really don't mind her i find her funny... her presence puts things in motion and she is so ridiculously self-centered that i have a little respect and just to remember aside from Hanako and the childhood friend (poor girl, i can only remember her by her status) are the only ones that really had a good introduction all the other girls had pretty complicated starts.