My guess is that while the women would be happy by adding a "non disclosure" clause in the same way that exist for adoptions, the extreme right who want to control women, won't be happy. And they would basically complain about the same they complain now: about women having sex "without taking responsibility". Which is also the same complain they have about contraceptives. And they would complain about taxes and having to pay for those phoetuses. I mean, they complain about free healthcare for pregnant women too even if that means more chances of a healthy birth...

The fact that there is no help for women who want to have children tells it all.