Scrapping a sanction against some solo mums will cost more than $100 million over four years and could result in fewer parents paying child support, ministry officials say.
Single parents who refuse to identify the other parent have $22 deducted from their benefit every week per child. After 13 weeks, another $6 per family is docked.
The policy was introduced in 1990 to ensure fathers paid child support.
The Labour-led government last year confirmed it would repeal the penalty, saying there was no evidence it worked.
A Ministry of Social Development report - obtained under the Official Information Act - said the government would pay out at least $25 million more a year as a result of ditching the sanction.
Officials said they could not predict how people might respond, but warned the cost could balloon, "potentially considerably", if people were then incentivised to rip off the system.
For example, mothers might choose not to name the father so he could avoid paying child support to the Crown and could instead pay her privately under the table.
Acting Minister of Social Development Peeni Henare said there was no evidence to suggest that might happen.
"This was a punitive measure... one that has actually proven to have no merit.
"What we're simply doing is removing it and saying that those who are on the benefit can actually receive their full entitlement that will help them."
He said the current penalty unfairly punished thousands of children in low-income families.
"And while it is a cost and we acknowledge that - it's actually the cost of ensuring sole parents are given their full entitlement."
However, National's social development spokesperson Louise Upston said the report showed the government's policy had a "dark side".
"Vulnerable women will be threatened with all sorts of things not to name the father.
"We don't want them under even greater pressure from a dad who should be paying and isn't."
She said the government was making a "very dangerous" move with no alternative.
Auckland Action Against Poverty spokesperson Alastair Russell said the MSD report showed vulnerable families were missing out on $25 million a year that they needed.
"That is money that goes into food, nappies, all the essentials of life that these kids in poverty need."
He said the penalty was an "appalling indictment on the welfare system".
"Punishing mothers for the behaviour or actions of fathers is brainless. It does not work."
Child Poverty Action Group spokesperson Michael O'Brien said the "narrow focus" on cost missed the point.
"Let's have a look at what the costs are to the children and families involved."
And he said National's argument that removing the sanction would increase the pressure on mothers was simply "scaremongering".
"I'm not seeing any real evidence to suggest that has any kind of substantive basis to it."
The MSD report noted that officials looked into the sanction's effectiveness in October 2016 and found it was "unclear" whether it had worked.
"The Ministry does not have sufficient evidence to confirm if the benefit reduction is achieving the policy's intent."
As of March 2017, more than 13,000 sole parents had been penalised, affecting nearly 17,000 children.
An exemption can be granted for reasons such as family violence concerns or the pregnancy being a result of rape or incest.