Economies of scale come into play here too. If you can get to the point where 2n is a typical job, then having two part-time jobs is likely to not offer as many benefits or long term opportunities as a single full time job. Even if n is a full time job, depending on the job, having one person work massive amounts of hours is probably better for long term promotion potential than two people putting in the bare minimum and constantly having to take time off to take care of children.

Also, as others have noted, a stay-at-home parent is not someone who "doesn't work at all." Most stay-at-home parents tend to be responsible for raising children, cleaning, money management, shopping, general home repair, and a host of other things that if you outsourced so that the partner could traditionally work, could potentially cost more than the partner's earnings.