Pat, not sure what you mean by "no other activities." I would venture that in my area, metro Charlotte, a private golf club with no other activities could not make it. The club I belong to, Carolina Golf Club (D. Ross, 1929), comes close, but, we do have a very nice swimming pool, and without the pool (remember it is really hot down here in the summer), we could not make it. So, we do have "other activities." What we don't have: tennis or other sports, a fitness center, "fine dining," or a "fancy clubhouse." (We do also have some special food and entertainment events - e.g., pig roast and club members' hobby band in connection with golf events, such as member-guests.)
You'd like to get the whole family into golf, but in reality it is the men, and the market here requires something for the rest of the family, and the pool works well. Maybe our GM, who's a member of this site, will chime in - he knows the numbers and has the pulse - I'm just speculating.
In any case, we have 500 members and a waiting list. There are four traditional, very upscale, full scale country clubs in Charlotte. Our initiation and dues are way less than half of theirs. I think that's a huge plus for us. There are also a number of newer "upscale" residential subdivision clubs (e.g., The Point, now Trump Charlotte), and many more moderately priced full scale country clubs. I can't speak with certainty, but I expect that all of the other clubs are below capacity.
Where do we "pledge" to spend money? On the golf course. Clubhouse upgrades, tennis courts, etc. are not in the picture. We run a very lean operation with, so far, no pretensions to social status.
In the past it's been suggested that we are a "starter" club - that as younger members become more prosperous, they move to the high end, full scale clubs. I'm an older (and old) member so I don't have a real good feel for younger members today; however, I have a sense that more and more, they may stick around.
As a footnote, at least two of the really high-end, full scale clubs here have recently spent, and continue to spend, lots of money on non-golf facilities. Obviously, someone at the clubs wants those extras, but from what I've heard the "golfers" are not all that happy about the spending.
In conclusion, based on my observations in my metro area, there is room for at least one golf club (with a swimming pool), but beyond that . . . I am glad that this is not a "business" that I am in.