Right now I'm not sharing my Ivermectin, lol. Just kidding.

I trapped a fox once that looked familiar to those pictures. He was hiding under a trailer house. There was two openings underneath.

So after setting a foothold in the narrow one, I placed a 330 in the other and blocked it off. Two days later took out the bad animal w/330.

Using a set of rubber gloves and two trash bags, placed him in the land fill.

The word "humane" implies that any and all animals should be treated as humans. I respect animals but I do not equate them with humans.

Maybe 'Taxing Authorities' will start charging them taxes on the resources they use like they do us.

One thing wrong with your theory and makes it easy for the haters . ALL animals will eventually die from disease, hunger or some type of injury. So trapping him as a way to "put them out of their misery" doesn't really hold water from a point of view.
BUT it will aid in stopping the spread of the mange so from that angle it could be promoted that you saved more animals.

The year MN had a wolf season. A trapper dropping off fur at my place had a photo of a wolf he trapped that was in the early stages of mange. Proof that wolves in MN were in the beginning stages of overpopulation.

Yes SIr, went to put out hay the other day and there was one froze to death in the hay shed absolutely eat up with the manage. About half of they you catch here have the mange.