I've been working with kleingrass on my own place and professionally for over 40 years. It is a "tri-purpose" grass, if there ever was one. With heavy management (fertilizer and weed control) it is very productive (not Tifton/coastal productive, but productive) for grazing or haying. I've seen cattle pass over Tifton hay for kleingrass hay. A 6 inch height is as low as you should ever go to maintain the stand. It can also work out in a "range" situation with no extra inputs, but the stand is more likely to thin. Letting it seed in the fall helps maintain stand thickness, even if it is a perennial, and it also means you've got growth for winter filler. It is a MUCH better standing crop in winter than any Bermudagrass variety. As far as wildlife habitat goes……..as a grass seed, it's like other grass seed for quail - better than nothing, but still not what quail really need. As a bunch grass, it's ok for nesting, but certainly no little bluestem. It does have the ability to keep green shoots underneath early in the spring, and I've seen many a deer grazing the tender growth. For soils, it does not like deep sandy ground, and likes good drainage in heavy soils.
Edit: Kleingrass has been known to cause "swell head" in sheep and goats, not sure about horse issues. I think it has to do with a fungus sometimes found in the seed heads.