In an interview with the Weekend Herald Ritchie said the decision for Ardern's partner Clarke Gayford to stay at home was "not the solution".
Ritchie, a former features editor at Child magazine and author of Roar - Like a Woman said just switching the gender roles kept "the old patriarchy firmly in place, while pretending to do away with it".
On a recent job-hunt in Australia Ritchie, a mum of two teenage sons, said she struggled to find something with hours that valued family life.
She believed Ardern was in a powerful position where she could make a big difference to the future of mothers in the workplace.
"I believe she is brave enough to do this," she said.
A part time PM sounded "wacky" Ritchie said but it would make a "school hour economy" more acceptable.
"The PM role surely has some trimmable fat, all those ribbon-cuttings, medal-awardings to the rugby under-14s, and...photo opps could be offloaded to others," Ritchie suggests.
"On duty, she could work from home, or bring Neve to the office."
Shipley said the issue wasn't about hours worked.
"In NZ women decide on their leadership identity and pathway and Jacinda is our Prime Minister - just as Helen Clark was and just as I was," Shipley said.
Shipley said it was positive that all three women Prime Ministers had differing family situations.
"How lucky are we to have three role models at different stages," Shipley said.
"Women who are leading, and exercising choice and having partners who support you in different ways."
That opinion was echoed by relationship coach at family support organisation The Parenting Place.
Jo Batts said what mattered was that babies had time love and attention from a special person.
"Jacinda and Clarke have taken on the full load of running a country and parenting as a team to make this a reality for Neve," Batts said.
"Women don't have the exclusive mandate for caring for kids, just like men don't have the exclusive mandate for leading the country."
Batts said Ardern and Gayford were setting a good example of teamwork.
"How running a country and running a family can co-exist with plenty of support."
Ardern was approached for comment on the opinion piece but staff members said she was not able to be contacted because "she was on maternity leave".