Serious answer - because it's not been tried on a major scale. Maybe it has worked for a handful of cases, but the models which were tried and worked to various extent at scale were: a) "village" - multigenerational joint families taking care of all the kids together, b) nuclear family - where moms stayed at home, c) nuclear family - where both parents are working and outsource child rearing to nannies and daycares.

If three-parent scenario is tried at a larger scale and if it works with small tweaks to our social contract, then why not?