I am no expert on Eplus, but unless New Mexico and her wildlife are just levels above everyone else, all these arguments of incentivization kind of fall flat to me given their neighbor, Arizona, doesn't privatize and they seem to be doing fine. The arguments I hear in defense of ePlus sound very similar to the arguments for privatization in MT, which would hose the working man in favor of the landowner.
Basically, it's all anecdote, which isn't nothing, but I have a feeling if NM abandoned privatization and went to a tag allocation similar to AZ, wildlife populations would not plummet. Habitats would mostly retain. I suspect the current situation is chiefly windfall for landowners, not an incentivization to meaningfully do things they wouldn't do otherwise. I could be wrong.