No, having a full-time designated room that is solely used for that purpose is not "legit and reasonable" when the infrastructure we have is already inadequate for the day-to-day work the military does. Do we put one in Base Ops? How about each of the aircraft hangars? What about the fuels building that is about 400 sq ft in size and sits on a pretty remote section of the base?
What would be "legit and reasonable" in this hypothetical situation: my wife comes to the squadron for something, brings along my infant child, and needs to breast feed. I find a solution. Briefing room, squadron bar, whatever. I don't know what "amenities" are now required, but women that are breastfeeding generally carry what they need. And if I couldn't find a private space that would work, I'd go ask someone with a private office like my DO or CC. You know what their response would have been? "You bet, Huggy. She can use my office."
In my 28 years of working on the flight line, I do not remember one time where a women came in and needed to breast feed. I'm sure it happens. But not with the regularity that requires that we give up valuable space. Space we need. Space that the US govt has been unable to provide us through MILCON dollars.
Here's a possible alternative: How about letting us find a solution to this "problem" on our own? A solution that isn't mandated though more regulation, govt mandates, or social justice warrior programs. Instead, I would rely on my mostly-male squadron mates to the be gentlemen that they are and to help out a nursing mother in need. In the end, we would do what we always did, and take good care of those that visited our squadron.