> four legs, ...
If we, as a society, want to encourage more kids, we should to allocate those funds as a society, much like roads or anything else (we do, tax benefits, ..., maybe we should do more). If we want to offer welfare for people regardless of their life constraints, that's again a societal decision (and one I'm mostly in favor of).
Pushing that to each individual employer sets up a cat and mouse game where the shadiest organizations barely not getting audited are able to leverage that inequality (supposing we did fix the wage gap at an employer level without addressing underlying factors) to achieve higher profits and outperform the competition.
And that's one of the _better_ outcomes. Switching gears only slightly, suppose (using round numbers for simplicity) the average cost to the employer of maternity leave is 6 months salary and you have a 10% chance of incurring that cost. An organization like the NYT can absolutely self-insure, but at the level of only a few employees you cannot.
Something kind of like the unemployment insurance situation works much better in those kinds of scenarios. The government acts as an insurer to provide the service we as a society have decided is worthwhile, and each employer only has to send in a check for their average liability instead of dealing with a different mountain of paperwork and existential risks.