Didn't mean to upset anybody, but sorry, it's my point of view.
Your are right to say " where there's life, there is hope". A starving cat still has a chance of feeding, a dead one doesn't..
It's too easy a solution to employ euthenasia
There are many alternatives and answers, but as always , it does cost money, resources and time as many people have already mentioned.
Jacqui, your point re cats keeping rodents down and also reducing food waste rings true . As a child , I used to visit my Grannies farm where they had four or five cats.none were spayed and were probably related. They were fed minimally in order that they did there jobs. Hunt and eat mice and rats that threatened hay, straw and animal feed.
Hugh.