Even if we take your argument on a face value, you seem to talk as if these extra "minimum wage" money don't matter.

 A full time minimum wage is some 2k a month in after-tax money - that's a significant sum to lose even in a "non-breadwinner" situation. Even if we go to a part-time minimum wage of 800/month after tax we'll see that few "primary breadwinners" will have no trouble getting an equivalent after-tax raise.