Yeah, this is real. Men still tend to get erased from the parental equation to a large degree. And this doesn't just affect stay at home dads. Much of the dialog around pregnancy loss and childloss seems to forget that there's often a father involved as well, and that the loss impacts both parents. When we lost our first child to a still birth, people would often focus entirely on my wife when offering sympathy and comfort. The assumption was often that I was supporting her through the loss, not that I was also someone experiencing the loss who needed support. This is problematic on multiple levels, but on a very basic level it just made it that much harder for me to grieve the loss and made me feel erased.

That said, I don't think it makes sense to connect the issues surrounding the ways in which men and women are still gendered in society, our resulting assumptions, and the harm they do with this particular problem. Because I think this particular problem affects both men and women, though with perhaps some differences in affect that are worth calling out because of the aforementioned gender roles and assumptions.

I haven't read the referenced book, but I would separate this problem from the one described in the book. I think we're reinforcing those stereotypes when we frame the general problem of "people not having work" as being specific to men.

Even beyond that, I would challenge the whole notion that people need to be included in the workforce. I think we're framing the problem wrong when we look at it that way. People need to be economically secure, they need to have deep connection to communities, and they need to have something meaningful to do with their time. Right now, many people only get those things from work. This is true of both men and women, plenty of women talk about loss of identity and struggle finding community when they become stay at home parents.

So I would argue that the book is taking the wrong framing - both in focusing on men and in taking the wrong assumptions, or perhaps, the wrong ordering.