That's an interesting idea, but a fair number of families don't want to do amniotic fluid testing. Paternity and maternity issues are pretty low incidence issues, but is VERY rough if it pops up with a 4 year old in the mix.

If you've got wrong dad in the picture, at birth is a good time to chase down the right father! Get him paying child support if needed. Non-bio dad could still decide to stay around if desired - but transparency / honesty on the table.