A glue trap isn't intended to be a catch and release trap. They are designed to hold the animal in place so it dies of thirst/starvation because it has no access to food or water. Pest control operators will routinely set them up, and come back within a week to dispose of the carcasses. There is nothing humane about them at all - what do you think happens when the animal gets caught on these things? It doesn't just lie there and wait to be killed, it tries to get off, often with horrific results. I am talking ripped off skin and broken limbs here since they struggle so hard but the adhesive is just too strong. So they will gnaw themselves out of it (eg. their legs) or even pull so hard as to leave patches of skin and perhaps a limb or two. The cruelty of these traps are well documented, if you would like me to provide you some links then I'd be more than happy to.

Interesting point about the instructions there, because for the most part they tell people to simply "discard trap with animal", presuming that one just throws a live animal stuck on the trap into the bin. You point out how other traps are banned for being incredibly cruel, when the glue trap works on exactly the same principle. The glue meshes to their skin, causing self mutilation due to the struggle of self-preservation, something that would not happen with a cage trap. They are like your other snare trap that captures the animal, holds it in place but doesn't kill it - though the means of the capture forces injury. That includes gnawing their own legs off to escape, and this is something that animals regularly do on glue traps.

Glue traps, in the end, cause as much needless suffering as a steel-jawed leghold trap for rabbits would due to the design of the trap alone. These traps should not be condoned in any way, in fact, they should be banned. The level of suffering these animals go through on these things when more humane alternatives could be used is simply unacceptable.