Not sure myself, but elk graze more than deer, so it maybe their gut is more accumulated to supp feeds than deer that browse more. There may be a biological difference rumen wise, not sure. I know there was a more deer friendly feed made, a pellet food, have forgot what was in it, but worked well. A ranch in WA used it for deer, the key is it was available in various amounts year round. Deer did great.
I suspect the key for any supp feed is accumulation time. But if the supp feed leads to an overpopulation situation, as it probably will, at some point a die off will happen, disease or what ever.