It's tricky to be sure what we are actually dealing with, and what the possible choices are with regard to Brucellosis in Yellowstone, because both sides in the debate are untrustworthy & devious on the topic.

Wikipedia's Brucellosis entry emphasizes that the disease transmits to humans and is serious. By inference, the more-fundamental threat to the cattle industry than the direct effects of the disease on cattle, is that infected herds would have to be destroyed, to forestall the threat of transmission to consumers.

There is a large U.S. Centers for Disease Control Brucellosis FAQ, which shows that the situation with this disease is broader & more complex than the Yellowstone Park dispute.

Will killing all elk & buffalo in Yellowstone free humanity (or even America) from the Brucella germ? No. It is a diverse problem, and global.

Are the herds of Yellowstone too large? By a large margin. "Ridiculous", if the mission is to preserve a 'natural habitat'. Instead, we have effectively the "Yellowstone Elk & Buffalo Ranch".

Would some like to see the ranching outside Yellowstone reduced or ended, so that overly-large populations of animals can be better-supported by having exclusive access to non-Park grazing lands? It does seem so.

Are the picturesque buffalo & elk herds being managed with a view firstly to tourism-values, and only secondarily in accordance with solid wildlife science? Sure. Many visitors report that their priority in coming to the Park, is to see the elk & buffalo. More normal population levels would be more-dispersed and much less visible. People see them readily, only because they are over-crowded.

The dominant token on this game-board appears to be the hope that by having over-large populations of these major herbivores, the chronic feed-shortage will disperse them seasonally into more & larger areas surrounding the Park, maintaining an implied pressure to treat regions surround the Park as though they are extensions of the Park ... when actually, they're not.

This is an example of the 'halo' idea - that Parks need to be surrounded by an ever-widening 'halo'-zone which falls effectively under Park-management, even though they are not Park and may actually have long histories of other usage.

The herds of Yellowstone ought to be a lot smaller than they are. That would greatly reduce the risk that diseased animals would travel far and thus expose domestic livestock to their disease. It would also take away a tourist-attraction (great masses of large animals in plain view), and disarm those who aim to use elk & bison to create an enlarged 'virtual' Yellowstone Park.