Fences were instrumental in the second Agrarian Revolution. Enclosing the land made it more productive meaning fewer farmers and more people leaving for the cities. Cheap fences like barbed wire just meant that you could apply it to wider spaces.
Enclosure only worked that way when there was already a substantial population living on the land, which was now surplus to needs, like in the Highlands. Since the Great Plains
didn't have a substantial (citizen, anyway) population in many areas, exactly the opposite happened: enclosure allowed more profitable but labor-intensive practices (primarily farming instead of ranching) to take place, thereby resulting in a growth in population. In fact many of the Plains states saw some of their most significant population growth
after the development of barbed wire: Montana and Wyoming both tripled in population between 1880 and 1890, just as barbed wire was being widely deployed, South Dakota increased three and a half and North Dakota over five times in population in the same time period, Nebraska and Colorado doubled, Kansas increased in population by half again, and Texas increased in population by more than a third.
If you continue moving forward, Texas has continued growing fairly rapidly up to the present day (although not mostly in rural areas, of course); Kansas stalled out from the 1900 census onwards, with much slower growth more reminiscent of other, more eastern states; Nebraska behaved similarly, with a dramatic slowdown in growth from the 1890 to 1900 census and continued slow growth thereafter; Colorado continued rapidly growing until 1920, then slowed into a more normal pattern of growth afterwards; North Dakota continued rapid growth until around the 1920 census, then shrank between every census after 1930 until 1980; South Dakota similarly stalled after 1920, then bounced around until 1990 when growth resumed; Wyoming and Montana similarly stopped growing rapidly after 1920, with Montana actually dropping in population over the 1920s before resuming fairly steady growth, and Wyoming merely slowing in growth. None of this is at all compatible with your hypothesis, which would suggest that the introduction of barbed wire in the 1880s would have driven population out of these plains states, when in fact they generally continued growing for another 40 years unless they were already heavily populated (like Kansas and Nebraska) where the ability to more cheaply enclose large areas of land might actually have driven some degree of displacement.
The pattern holds even more strongly if you drill down to the individual county level, historical population peaks in the Great Plains came largely between 1910 and 1930, with a few counties in primarily Kansas and Nebraska peaking in the 1900 census. Again, this is completely inconsistent with the idea that a technology developed forty to sixty years earlier was the cause of the displacement. This makes sense when you realize that the primary effect of barbed wire in the Great Plains wasn't to allow more efficient large ranches, it was to allow the subdivision of land into much smaller and more intensively operated farms owned by individual families, which results in a higher population density than small numbers of large ranches relying on extensive grazing practices and (single male) hired staff. If anything, the timing of the historical population peaks strongly suggests that the economic stagnation experienced by agriculture in the 1920s (probably for fundamental structural reasons) and the Dust Bowl and major drought of the 1930s are primarily responsible for depopulating most of the Great Plains. Neither of these, obviously, had all that much to do with barbed wire, except that it maybe enabled some of the bad farming practices that led to the latter.