DD's school used this system. They didn't seem to understand that her 'bad behaviour' was her simply not understanding/being able to act on their expectations.
In pre-school she had no 'behavioural problems'
In year 1 she got 3 demerits for 'being disrespectful to an adult' - the same number as she would have got if she got into a physical fight with another pupil. Her crime was not answering a teacher's question. I met with the teacher at the start of the year and explained that DD 'shuts down' when confronted - it is a trauma response from the abuse she experienced in her birth family.
She said to me in year 2 'At school I always feel as if I am about to be told off, but I don't know what I am doing wrong'.
By year 3 she was self-harming in school (she would hit herself in the face) - and I was told that it wasn't fair for the other children and teachers to have to be exposed to this.
No other school would take her (we weren't in the UK), and I couldn't afford to go private, and as a single parent I couldn't stop work to home educate.
She is now in a lovely school who realise that rewards and punishments have little impact on behaviour, because the majority of the time those with repetitive 'bad' behaviour are not making a rational, calculated decision to behave 'badly', so are not sat there calculating rewards and punishments. They are reacting to their environment.
She has been diagnosed with PTSD, with the way she was treated at school number 1 contributing and increasing the impact of the abuse she experienced in her birth family. She is gradually beginning to trust some of the staff at school, 2 1/2 years in.