Don’t forget that those societies also impose heavy obligations on men. Are secular women, many of who are stuck both working and raising kids by themselves without men supporting them, happier on average? I haven’t seen any data to suggest that’s true. Indeed, Mormons are happier overall than other groups: https://news.gallup.com/poll/152732/religious-higher-wellbei.... Maybe there’s a big gender gap there but I’m not aware of any data to support that notion.