>

You can throw in a small backyard chicken coop and still get eggs too. No animals are dying that way, it's essentially a chicken period. But provides much the same proteins as meat. And you can personally provide much better care for those chickens than the chickens that are producing the eggs for the store, so I think it still falls under ethical.
It’s great and I say that as a hunter myself but it’s only sustainable as a niche activity, imagine if everyone hunted… >

That is absolutely true, but I was talking more about the nature of hunting >

So obviously it isn't true that it is the most sustainable, as it is insufficient to feed a population of any size. It's like pointing out that collecting paper scraps and pulping, forming, drying, and pressing new sheets yourself is more sustainable than buying a box of new paper. Sure, it is, but that isn't really a realistic solution to any problem >


Economical efficiency:

I pay $300 for an out of state deer license, then $1200 to a rancher to hunt his property and sleep in his old RV.
That is $1500 so I can get maybe 50 pounds of venison. That's $30 per pound of meat! 
I'm not even bringing up the cost of the rifle or gear.
That's great you live near a place where elk is prevalent. Most of us don't. >


I pay $300 for an out of state deer license

Thats alot.  Out of state licenses in my state are $115 and come with 2 tags.  You can even save $20 if you bundle in your non-resident fishing licence. >


most sustainable, ethical and economically efficient way of gathering food

I'd reckon that the most sustainable would be one where you cannot over hunt your prey. If everyone hunted, it would no longer be sustainable as a viable food source. Depending on you ethics, the most ethical would be to not eat meat at all. Even if you are ok with killing animals to eat, "what is ethical hunting" is a debatable thing with some saying that only "Fair Chase" hunting is ethical and others saying that blind hunting and baiting is ok. And, for the economics: training, gun, clothing, license, time spent, transportation, processing, storage all add up very quickly. It would surely be more economical for you to just buy some meat from the store.  
Honestly, the most sustainable, ethical and economically efficient way of gathering food is to be a locavore vegan, eating no meat or dairy or eggs, and sourcing all of your food from an organic home garden and from organic farms within a limited geographical area from you location. >

I think your view makes sense on an individual level but the problem is it doesn't scale. For instance you say that an elk could feed a family of 4 for 3 months so let's use that metric. The total elk population in the US is just over 1 million...elk would be extinct within a month...deer are a bit better off with around 35 million but even if they fed as many Americans as elk do and even if we hunted the elk first all the deer in the US wouldn't last a year.
All of this is to say that you're right: hunting is sustainable, economical, and efficient BUT it doesn't scale. There simply are too many people for too few animals. >

It depends on what you hunt, hunting deer and such for food is fine, but shooting wolves out of the helicopter is just sick. >

I'm no environmental scientist, but it seems to me that growing your own fruits and vegetables and eating them while harvesting and replanting the seeds would be more sustainable, ethical and economical than licensed hunting.
Sustainable - You're controlling your own sustainability by harvesting seeds rather than relying upon nature to replenish your hunted animals.
Ethical - None of God's creatures has to die.
Economical - After the initial, minimal investment for seeds, there is going to be minimal cost.  It could even be zero cost with proper crop rotation and composting.  You'd need some land, but you need land for hunting as well.  And I'd imagine that hunting would require far more acreage than subsistence farming.