Not sure who you think shoots elk in alfalfa fields, but I never have?
You sound confused.
Can you point out the alfalfa for all of us in any elk hunting picture I have posted, and there has been many.
The following picture is in a juniperous osteosperma stand, commonly called Utah Juniper. Utah Juniper is a tree, not a forb in the legume family like alfalfa. That fluffy stuff in front of that bulls neck, that is a grass, one of the native sedges to Wyoming.
This look like an "alfalfa" field to you? That is actually sage brush. Under that snow, there are several species of grass that elk find quite palatable. At least 2 species of fescues, a gramma, and a sedge or two.
This elk was in a stand of Quercus gambelii, also a tree species in the interior west. I can understand how you may confuse this one with a shrub, but it is classified as a tree species. If you try to hunt, shoot, or pack elk out of a stand of Gambel's oak you probably will not forget it.
This elk was shot in a mixed stand of Spruce, Subalpine fir, lodgepole and aspen, those are trees. Lots of grasses, mostly pine grass, some sedges again, 2 species of timothy, and likely even a poa or three. While this is a much wetter site than the above pictures, there is clearly no alfalfa anywhere near this place. Would be tough to get the permitting in designated wilderness to clear that area for alfalfa, divert the nearby creek for irrigation, and doubtful the required farm equipment for the job would be allowed.
If you need any further clarification on what alfalfa looks like or you're unfamiliar with the varied habitats that elk call home, by all means, don't be afraid to ask. I'm here to help, in particular with the clueless and for those that are much better at shooting their mouths than elk.