In the early 2010s, Bay Area startups were famous for "unlimited vacation" policies that resulted in less overall time off because everyone was well aware that taking even a standard amount of vacation would signal a lack of devotion.
What's the solution? Mandatory benefits: make everyone use their allotment, even if they don't want to. Many large banks force all staff to take holidays not only to combat a culture of overwork, but also to prevent fraud by making sure everyone has a block of time where they have to hand over their work to someone else.
If the Japanese government were truly serious about the "ikumen" ideal, it would pass a law requiring 6 weeks of paternity leave. Of course, I doubt that's politically or culturally feasible.