[Trilkhai]

The studies I've seen showed correlative links between m/paternity leave itself with improved psychological results, not necessarily ones that are specific to reproductive rather than personal leave or aren't also tied to the workplace/society having better social support. Somebody with an employer or in a society that allows people X weeks/months off for personal reasons -- whether it's a matter of choosing to reproduce, finish a degree, caring for an ailing loved one/pet, or combating burnout -- is likely to fare much better psychologically than somebody required to work continuously regardless of their personal circumstances.

An interesting parallel occurred a while back when there was sudden widespread adoption of Finland's "baby box" of supplies for new parents after the BBC noticed that Finland's infant mortality rate plummeted after their introduction. The results have been lackluster, however, because people had overlooked that the improvement in Finland had been tied to a whole bunch of policies & healthcare changes, with the box being only a tiny part of the result.