To get back on the subject, while decease and loss of habitat might have contributed to the extinction I would say that hunting was what finished them off. The idea of taking “one or two per year” is contrary to the hunting methods used against large herd animals at this time, which was to drive the herd over a cliff. This allowed you to get maximum bang for your buck and kept your hunters from getting killed. Keeping your hunters healthy was a major consideration when a large band might have 100 people in it with maybe 25 hunters. Most were smaller with 10 to fifteen hunters. Losing even one was a serious loss to the tribe.
This was the method used against the buffalo and the buffalo population was steadily shrinking until the arrival of the horse when it became possible to hunt a few as needed. And buffalo have a much shorter cycle then the mammoths probably would have. Four years as opposed to twenty years I think.
a.cricket
When I was in second grade or third, I attended an art class and learned how to draw. My drawing has not progressed significantly since, but the interesting thing was this other kid, a marginal retard. He wasn't smart, not even for a second-grader, but he didn't know anything, really nothing. Most kids know some stuff, he knew nothing.
He wasn't able to draw or do anything with clay or mache, just a total dunce. But one day we were asked to draw an elephant. Surprise! He drew an elephant, rendered in 3-D shadowing and texture, great range of color, and it was just a great-looking elephant. Then we went to clay and he made a clay elephant if anything even better than his drawing. I asked him how he learned to draw elephants, and he didn't know. He just always could, but nobody ever asked him to, so he never did.
Perhaps he was descended from a group of mammoth hunters a few eons ago. Something like mammoth-hunting would have to be almost genetic, you would have to "know" how the mammoth works, how it thinks. Bet that kid would have been a mammoth hunter.