Was it necessary? Hmm. Interesting way to ask this question. Let's consider a few things.

First, U.S. motivation. The United States during the Great Sioux War was still recovering from the Civil War and the Reconstruction of the South.

When gold was found in the Black Hills in 1874 by George A. Custer, a move was made to separate the Black Hills from the Sioux. Many settlers continued to head west and follow the gold rushes going on in other states and now, South Dakota. Because the land belonging the the Northern Plains Nations was still in their possession, this put stress on the U.S. to provide protection for these settlers and travelers. Rather than keep up their end of the treaty, numerous violations were made and a bid to "legally" buy the Black Hills had commenced.

In order to really understand the situation the U.S. Army was facing when fighting the Plains Nations, we've gotta look the context. Tensions were already high between the Plains Nations and the U.S. Government. The Second Treaty of Fort Laramie was signed in 1868 to bring an end to Red Cloud's War, which ended in defeat for the U.S. after several losses. In the years prior to the start of the Great Sioux War, it was a supposedly known that Sitting Bull and the Lakotas were "gathering in force" and had been collecting weapons and ammunition, among them being Winchesters (I speak about this somewhat in a previous post, check that out here). According to some statistics, around 20% of the 577 men in the 7th Cavalry were considered recruits at the time of Custer's Last Stand.^[1] Going even further, only 172 men, around 30% of those total troops, could claim to have fought Indians.^[2] In fact, even the quality of these soldiers' training has been called into question.

Now take all that apply it to most of the Army units patrolling the Plains at this time. The desertion rate all around was around 30-33%. Many officers at this time were subject to alcohol abuse, many doing so as a result of the horrors of the Civil War. When we look at all of this, the previous defeats, the poor training, the lack of experience, and the armed tribes, it is not hard to see that the U.S. Army at this time was not particularly keen on fighting Indians and winning without taking significant damage, despite the braggadocious attitude of likes of Custer. It is because of this that they decided to change tactics. Rather than take the Indians head on, a war of attrition would be waged - nay! A war on the buffalo would be waged!

After the signing of the Second Treaty of Fort Laramie, the U.S. Army supposedly only pursued natives who roamed beyond the established reservation boundaries of the Great Sioux Reservation and the allotted hunting grounds. In 1866, General William T. Sherman assumed command of the Division of the Missouri, including the Great Plains. In 1869, he succeeded Grant as commanding general. Sherman had a great deal of experience when it came to war. Being personally opposed to some of the concessions and agreements made at the signing of the treaty in 1868, he believed that subjugating the native would be the way to go. Included in the purview of his command was also the construction of the railroads that would soon pass through the Plains. It was of utmost importance that Sherman see that the railroads would be built. This is because they would play an integral part in executing the same methods he utilized during the Civil War.

Rather than fighting the Sioux head on, he targeted their food source - the buffalo. You ask if the U.S. Army could've afforded to do this... They most certainly could and did. I wrote a comment recently that actually explains this in great detail. Check that out here.

Based off Sherman's plan, the move to bring the Indians to their knees eventually succeeded. However, the ineffectiveness of the U.S. Army was still seen in the Great Sioux War, with the decimation of Custer and his 7th Cavalry being the prime example. Many tactical and strategic mistakes were made, including the actions of Reno who put him and his men at a disadvantage. Custer himself also seemed to underestimate the force he was dealing with. Combined with numerous other factors, though, natives could not hold out for a prolonged war and eventually gave in and were forced to move to the reservations.

As for the logistics of the tribes, a bit can be inferred from the posts I linked. Many of their weapons came from previous trade agreements, raids, government handouts for hunting, and both legal and illegal trading. These tribes were sustained by the buffalo herds, so their food and supplies came primarily from these animals. They had to move with them. Whatever else they needed could be obtained through trading with various other tribes or trading posts. Transportation was the horse and travious.

With the intentional killing of the buffalo herds, sustaining themselves through winters became harder and harder. That was their source of food and basic materials. In fact, when Sitting Bull fled to Canada, one reason for his return was because there were not enough buffalo up there to go around.

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Citations and Sources

[1] They Died With Custer: Soldiers' Bones from the Battle of the Little Bighorn by By Douglas D. Scott, P. Willey, Melissa A. Connor

[2] A Terrible Glory: Custer and the Little Bighorn - the Last Great Battle of the American West by James Donovan

My main sources for this, besides the citation for numbers, was A Terrible Glory: Custer and the Little Bighorn - the Last Great Battle of the American West by James Donovan and the sources in my previous comments, linked above.

Edit: Reworded a sentence.