but a payor has a right to provide for his [or rearely ] her children as well - or new families.
No.
The payor knows they have a financial obligation to their existing children and this information should be used when determining to have a second family.
If the payor chooses to have another family, their obligation to their existing children should not diminish due to their choice. Having more kids or a second family is a choice. And ones responsibilities don't change because of bad decisions.
Think of it as buying a car. If you can't afford it, don't buy it.