a. Every child is legally entitled to be supported by both their parents
b. Regardless of what may have happened in a marriage or partnership, is certainly isn't the child's fault they are resident with one parent, and it has no bearing on their entitlement to be supported by both parents.
c. Child maintenance is payable to whichever parent has primary care of the child. The law doesn't discriminate in that regard.
d. Where do you get your figure of 'thousands who pay nothing at all'?
e. It is up to the primary carer to both obtain and enforce the child maintenance payment.