Cage traps like snares, traps or M 44's all require a different methodology. The above photo is perfect in showing how unattractive a live trap is to a coyote as it associates it with something that triggers the wary response, and the attractant is not convincing the animal to approach.
Just as with snares in electric fence agrarian areas make coyotes wary, the cage trap requires to be placed in a situation which it is blended in, and not sticking out like a double longspring trap.
I am not saying live traps are easy on coyotes. They require big footage and approaches of blending and attractants. As in all trapping, you are going to only skim the Darwin candidates not having a good day. The statistics on all capturing of wildlife is variable. The cage trap has less practical public information posted, so it's capture rate is lower. It will never approach the ease of a steel trap nor the ease of a snare or the convenience of a getter. It will though in niche crafted situations will produce. It just needs it's own version of a Dirt Hole, trail or mound to bring the odds up.
The good government trappers of a generation ago, relied on poison and aircraft to make control work easier. They still did not exterminate coyotes and only kept them in check. They did not publish their methods and those trappers who have studied cage traps for coyotes never publish their success as it does not prove to be wise to educate coyotes or your competition.