Sovcits have actually showed up at hospitals before and CAS has gotten involved. One was a sovcit couple who were trying to deliver baby themselves out in the woods in a state park in Kentucky I think; labour stalled after 2 days so they finally came in, and during the admission told the hospital staff they planned to move back into the tent with baby when born, which was during the winter, and refused to get baby a birth certificate or give him a name, so CAS took him and their rights were eventually terminated and baby adopted out. Dad later got arrested at a library for threatening people, and they still have Facebook page demanding his return several years later.

There's also an OB nurse who has a great Tiktok about obstetrical care and birth, and she says she has helped deliver three sovcit moms after they finally gave up trying to deliver unassisted and came in, and two of the babies didn't make it.