The solution to the financial support issue for children in such a situation is simple:
Change the child support system to make it equal and free of gender bias.
If ONE parent is obligated to pay child support then by law BOTH parents should be obligated to pay child support.
Then there is equal protection of the law for the child — whose parents both must make a documented financial contribution into a state-held fund for the child.
The state child support agency collects payments from BOTH parents and then allows disbursement from the fund by each parent according to the needs/expenses of the child, the division of parenting time/custody and the income of the parents. Each parent has a debit card and a monthly maximum; at year end there is an audit to ensure that the funds have been used for the direct/indirect support of the child. Surplus fees are available for unexpected/variable expenses or will be disbursed to the child upon reaching adulthood.
Either parent or both parents would be considered deadbeats and subject to criminal prosecution of they don’t make their child support payments.
A father or a mother who is employable but chooses not to work would still have to make a monthly payment. No mother can use child support payments by the father to support herself.
Then we have an equal system that protects the child’s interests.