In a number of ways. First, it will create powerful incentives to women not to have more children than they can “afford.” The private safety nets may well refuse to assist a genuinely irresponsible mother. By “afford” I mean that a family will not have a marginal child, if the parents feel that this child will impair the standard of living of both the parents and their existing children “too much,” i.e., below what they find acceptable.
Second, it will strengthen the institution of marriage, insofar as women will know that it is in their interest to have a provider for them and their children. No public welfare here!
Third, it will eliminate taxes, thereby easing the burden on the majority of the population.
Fourth, it will create ever greater prosperity, thus, e.g., making day care, if such a thing is desired, more affordable. Both (3) and (4) will reduce the utility of a second income from the mother’s wages. An average man should be able to support his entire family on his own paycheck alone. This does not mean that women ought not to work; merely that they will have an expanded choice about what to do in life.