Would be interesting to compare just how urban the Golden Age country club member was. It was called a country club for a reason, and at the time, was pretty far out of town, sometimes on a rail line for ease of access. Did the typical member live on a small Chicago (or name your city) lot and go out for weekends?
My point is, America being progressive, and having more single family homes with yards now, more parks, more lots with golf in the backyard, maybe the nature thing has diminished over time for a few reasons. One, more golfers have their own little slice of nature (or approximation of it) and two, I think in general, "nature" is more pre-processed for us than it used to be, much like our food has gotten more pre-processed for ease of consumption.
In other words, we might have a different view of "nature" probably expecting/accepting something less close to nature as "natural" compared to a golfer in the 1930's.
And, landscape architects and maintenance folks continuing to get our impersonations of nature more and more perfect and "sanitized." This includes golf. We now call parks open space, not natural space, and real nature is called a "Wilderness Preserve" (to be seen and not experienced?).
I still believe television has sort of compromised our thinking, as we compare nature to what we see on TV, and not the other way around, since we spend more time with the latter and it becomes our frame of reference. And, it has made us demand more things that are easily understood visually, and quickly.