Similar devices have been used with sodium fluoroacetate ("1080") in Australia, which is even worse in some ways -- sodium fluoroacetate is less immediately lethal, but there is no known antidote.
There's evidence that suggests that efforts to control Coyote populations by killing them off are less effective than we thought - as the Coyote population drops in one area it creates a vacuum filled by coyotes from another area + increased reproduction, resulting in areas that underwent "coyote control" having spent a lot of time/money/effort and being back where they started at the end of it.
I can't verify a word of this, but I found the possibility interesting.
(I'm generally against any indiscriminate traps like these. I'm fine with hunting coyotes, but a device like this is too much of a risk to non-coyotes - as other commenters have already pointed out.)
Regarding private property, what guarantees that people will remove these when they move? Or remember where they put them? I remember finding old school traps on my parent's land growing up, left there by a previous owner. Most were not loaded or rusted beyond operation, but some still snapped when you hit them with a stick. From the pictures, I'm not sure I'd spot one of these devices while running around in the woods...
For the same reason I'm not allowed to duct-tape a shotgun to a chair and tie the trigger to my doorknob.
"The grower groups emphasized the economic losses associated with predators killing livestock and reiterated their position that M-44 devices were an important tool for protection from coyotes."