Availability is only part of the answer. As article notes, even when it's available, far fewer men take it. In my experience, it still comes down to the known hit to your career. I worked for a large tech co. in a "liberal" city that offered generous parental leaves. Most new mothers took many months off. Fathers, if they took p-leave at all, would take it in small chunks. Not having to leave work for a long period helped their career growth/trajectory tremendously.

I’m curious which company and city this was? Because I also work for a large tech company in a liberal city, and almost all the fathers I’ve worked with took at least some paternity leave, although less than women.

Or if they take leave, they don't take too long. I've noticed that father's tend to return in one month. They all say they got bored but what I think is they are afraid of reprisal.

Nyt lives in a bubble

Researchers are not stupid. They did try to control for social class, although it may have failed due to data limitation.