The water history of southern Idaho was somewhat different. The Oregon Trail passed within a few miles of my house. Tens of thousands of immigrants went across Idaho and never looked at the land because it was too dry. The Homestead Act didn't work here. It was designed for dry farming and for those few lucky enough to file claims on land with springs and streams. Around 1900 congress passed a modified homestead act called the Cary Act. Besides the free land like the original act, it also allowed settlers to form water corporations to develop irrigation dams and canals and then sell shares to get the water to the land. It worked and allowed Idaho to develop millions of acres of desert into very productive farms.
Like other western states, water law is everything. It's a specialty field of law and it's what keeps the entire area alive. We had another thread about the dams on the lower Snake River (after it leaves Idaho) blocking the salmon runs. Every drop of the Snake River is appropriated. More land can't be developed because there's no more water. Many farms are pumping ground water but a few have been curtailed because their pumping is slowing the flows from springs where someone else has senior water rights. It's a very complicated mess.
