I hear what you are saying OP.
It is this bit She is never rewarded for the good but is punished for the bad.
I was only thinking the same yesterday when I found my dd had picked up another behaviour point.
She never had any in Yrs 7 - 11, but has moved schools for 6th form and they are clearly very much stricter in this school. I don't particularly have issues with them giving out behaviour points (usually in her case because she has forgotten something - she has real difficulties with organisation).
I personally don't think it is the best use of teacher time to be constantly recording everything, and not being allowed to use their professional judgement, but it is what it is and presumably it means it is consistent for everyone but if they are going to be giving out behaviour points for every thing a student doesn't get right, then the 'positive points' ought to be given out with the same freedom and regularity.
That is what doesn't happen in dd's school - and it would appear, in the OP's dd's school. There HAS to be a balance and plenty of the positive points for ALL the dc that go through every day arriving on time, no back chat, no 'attitude', no pushing boundaries on uniform or 'cheek'..... the dc who are polite, listen well, hold a door open, help someone out, go the extra mile, volunteer for something - even something small such as an errand within school time.
Of course my dd isn't perfect - and I'm sure OP's dd isn't perfect, but ALL dc who behave, should be getting positive points regularly if the school wants to make 'behaviour points' a thing.