The sanction on solo mums who refuse to name the father of their child is making life harder for 16,842 children in low-income households, a government report shows.
Ditching the sanction, which the Government has signalled it will do, would cost $100 million over four years, according to a report from the Ministry of Social Development.
But ministry officials also warn that the costs could be "potentially considerably" higher if levels of compliance fall - a possibility that the National Party has previously warned about.
The advice is contained in a November 10 report, released under the Official Information Act. The report notes that it is unclear whether the policy is working as intended.
The sanction was put in place to encourage the establishment of paternity and child support payments from the father. Failure to name the father sees a $22 weekly penalty on the solo mum, increased to $28 after 13 weeks.
Several exemptions can be granted such as if the mother is at risk of violence, or if there is insufficient evidence of who the father is.
Social Development Minister Carmel Sepuloni has said that the sanction unfairly punishes children in low-income families, and there was no evidence that it had any impact on absent parents paying child support.
"We know that has had a negative impact on the woman and the child."
March 2017 figures show that 13,268 working-age solo parents have a benefit reduction in place, decreasing incomes in households for 16,842 children.
In October 2016, officials said there was not enough evidence to show whether the policy was working, the report said. Research from the 2000s also showed that many beneficiaries did not understand the policy, and anecdotal evidence suggests that this has continued.
The report also warned that repealing the sanction could be an incentive to rip off the system. For example, a solo mum could decide not to name the father, who could then pay child support privately.
The National Party has already warned that removing the sanction may push fathers to pressure mothers not to name them.
"Clearly there's an opportunity for a father of the child to put pressure on the woman to not name him, so he doesn't have to contribute," Opposition leader Bill English has said.
"It fits in with the notion around child support that the absent parent, generally a father, has responsibilities. The system can't enforce those responsibilities if they don't know where they are."