There is statutory provision to do this, but usually it is not applied because realistically, once you exempt all the parents who would be entitled to it for free, e.g. benefits recipients, plus all the children who would be entitled through other funding, e.g. children receiving disability support, children on probation, children receiving time-limited emergency care, plus all the people who would receive discretionary exemptions, e.g., where it would create financial hardship for other children remaining in the parental home, then you are left with only a small group who would need to contribute.
You then have to decide what it would be reasonable for parents to be charged for, so it wouldn't be the full £3,000 but only a proportion of that for things like bed and board.
Then you means test your small group of eligible, but not usually all that well-off, parents and charge them a proportion of the smaller figure. Meaning that it doesn't generate much actual money.
Then you set against this the cost of enforcement, plus the opportunity costs for both the child and their families related to missing the opportunity for earlier intervention amongst those who don't engage and for providing other support to families who face financial hardship as a result of having to pay.
As a result of all this, it largely comes down to a moral decision, with on one side the case that parents should pay to support their children if they are able to, and on the other side the case that the welfare of the child should come first and that there should not be a financial element to decision-making around the welfare of a child. A worst case scenario would be a situation where one child was being looked after but an equally if not more vulnerable child was not, because the first child's parents would contribute to the costs, but the second child's parents wouldn't.