I think that there are two components to this.
1. A minimal effort to dispose of remains on an occasional need-to-know basis, and
2. The larger decision not to disclose to the American public that they are known to exist.
The first aspect is made possible by public skepticism. Even if a dozen or so people see a dead bigfoot, and someone comes along to collect it, and even if there is eyewitness testimony and cell phone footage, the incident is generally regarded by the larger public as either a hoax or an urban legend.
The second aspect must be avoidance of societal disruption. I agree, if environmental activists during a liberal administration gleefully leveraged the spotted owl, you'd think it would be ten times worse with bigfoot under the current administration. But that hasn't happened, so there must be one heck of a perceived downside. We know that in the case of alien life consultants advised the government against public revelation due to projected societal disruption. Without linking bigfoot to aliens or UFOs, there are some arguable parallels to how society may be projected to respond to the revelation that bigfoot exist.
I, for one, believe that the government is incapable of controlling them and that society would demand that they do so. Revelation would also require classification and potential grant of "human" rights. How do you deal with them then? I believe that enough of the public would regard them as dangerous that the government would be under pressure to assure public safety and at the same time another part of the public would be demanding humane treatment. You can't control the bigfoot (if you could, what would you do, put them on a reservation?), and you can't deny public access to every place bigfoot may be, so why put the government in a position where it has to deal with the issue and the associated cost, which has probably been projected to be the same as conducting a small war?
Even if a number of human lives are lost every year due to Missing 411 type scenarios, from the governmental perspective it may be regarded as an acceptable status quo based on simple economics, but only so long as the public remains clueless.