I think a mix of accommodations, from primitive to luxurious, is acceptable and can think of perhaps a few other locations where the less than primitive "improvements" could attract responsible use. Remember, part of AMC's mission is educational and there are many hikers who get their first, if not only, introduction to leave no trace ethics and hiking safety. Places like huts also make it possible for some people to hike when they might not otherwise be able to enjoy such places. Are we such self centered snobs that those people don't matter?
At a time of increasing numbers of couch potatoes and virtual reality nerds buried deep in a digital screen, outdoors numbers are diminishing. If another hut contributes in a small way to reversing this trend and encouraging better fitness and more conservation awareness, I'm all for it.
As for the economics of the huts, there are three factors to consider. First, unless you've run a business you probably way underestimate the cost of operation. Second, there are many AMC activities that are not revenue producing and whatever produces revenue for activities such as education and conservation make those parts of its mission possible. Third, a non-profit is not defined by profits and losses but by its charter for a public good and the fact that it doesn't have "owners" who expect a return on their investment. No organization, profit or not, would survive for long without revenues in excess of their costs, no matter what you call it.
I second David's invitation to let us all know how the books are cooked. There are organizations that do it, unfortunately, and you'll find plenty of detail to work with in any non-profits' financials which are easily accessed by the public. I can assure you, there are brighter and more dedicated analysts than most of us looking at these things on behalf of major donors.