I honestly don't see how that would work. Animal food is already made mostly from the garbage/scraps off the butchers' cutting table. The parts people don't want to eat anyway, and it is sold to them very cheaply.
If dog food companies are already at liberty to use hog meat (I assume), as much as they can hunt and for free, but they do not choose to, how are we going to convince them to do it for a 'nominal fee?'
By nominal fee I mean a relatively insubstantial to cover the processing of paperwork, something on the order of $100 or so, which would give them exclusive rights to commercial harvest on a given size parcel of public land (let's say 10k acres?).
At present I believe that they can not do so now because in most cases commercial use of game animals is not permitted.
You don't see much venison for sale at the local market, and the little that is sold commercially is farm raised not wild. While these are not considered game animals per se, I don't think their meat falls under the same rules as farm raised meat in regards to the Dept of Ag or the FDA.
I suspect the issue is legal or regulatory rather than cost effectiveness.
If a pet food company operated a series of pen type traps and was getting the pork for the cost of the pens, transport and slaughter of the hogs, plus $100 I imagine it might be profitable. Might need to be a "premium, all meat" dog food.
Heck, it could be used to make high protein chicken feed AFAIK.