I don't understand how a government app fixes the problem.
I've talked with women about this offline and they usually fire back with: "You expect women to lower their standards?"
Women would rather delay pregnancy until they find a suitable partner, than risk being with the wrong guy.
The only thing I _maybe_ can think of is governments could only show profiles in your 'tier' (looks, social economic class, etc), whereas private dating apps found that showing everyone pretty people keeps people coming back.