That's a stretch as an explanation and doesn't fit the data. The resumption of rapid population growth in Arkansas in the 1870 to 1880 timeframe suggests the explanation is incorrect. As a frontier state, Arkansas should have been growing rapidly, just as it did later.
I've read of what a wasteland portions of Arkansas became during the war, but I assumed they recovered quickly after the war (although I had also read some accounts that they did not.) The 1870 census suggests they did not recover rapidly.
If you look at other frontier states, they grew rapidly as well. This includes Kansas. Having lived in both Kansas and Texas, and having made a number of vacation trips to West Texas, I can assure you that Kansas windmills are a signature feature.
I'm not sure what the point is with the Gold Rush comment of the contention about public lands. As you can tell from looking at census figures, the other states grew rapidly as well. Considering relative land mass, Texas' growth looks rather normal.