I believe that feminists are responsible for "the nanny problem" but there is a large difference between attributing it to feminists and saying they are to blame for the problem.
Tronto questions to what extent a social movement can be to blame for the societal ills that are a byproduct of it. Because women were able to join the workforce along with their parnters they needed someone to take care of their children, so they brought domestic workers (or nannies) into their home.
An easy alternative to this would be sending them to childcare. This eliminates the ills of domestic labor and the strange congext of working in someone else's home for that person.
In the 3rd contention of "I want a wife" it outlines the creation of the dilema that tronto writes about. That the desire for economic independence, and joining the middle class have necessitated some form of child care.