Our first mistake was to eliminate the natural predators because they were killing "our" animals. The natural predators, wolves, are not selective hunters. They do not care if it is a doe, fawn, sick, weak, or a healthy and mature buck.
Shoot more does and only mature bucks. By doing this you bring the buck to doe ratio closer and it begins to resemble the natural world, before we showed up and botched it.
It seems inconsistent to me to argue that natures way is not selective and then propose a highly selective hunting strategy to more closely "resemble the natural world". If we wanted to get closer to your view of the "natural world" the herd would be better off if each hunter would adopt the if it's brown it's down philosophy. If everybody just shot the first deer they saw it would much more closely approximate a random kill than a stategy that very selelectively targets mature buck and females. Said another way, a strategy that selectively protects male deer with small antlers.
I disagree with your premise in the first place though. I don't believe natures way is random. I believe it is highly selective. Natural predators seek out the easiest to kill. The weak the sick and the young are usually the first to fall. The big mature bucks are the lowest on the predators target list. So it seems to me if your goal is to more closely "resemble the natural world" then proposing a strategy that targets the mature bucks over the imature bucks and femalesis bass ackwords!
Now if your goal is simply to improve the probability that a hunter will get the opportunity to kill a mature buck then I think you've got a winner.