Why should locking up child abusers be controversial?
Automatic genetic testing also has other advantages of preventing future paternity disputes.
Honestly, this would be an interesting thing for a single state to run an experiment with and see how behaviors change.
Given women cheat at the same rates as men, blanket genetic testing would break up a significant amount of families. That's why some countries (France for example) ban paternity tests.
Ending abuse for the pregnant girl is certainly their prorogative