Homeless cats should NOT be killed!! They should just be neutered and then let to live as free, if rescue groups didn´t menage to find a "real home" for them. Cats who live outside, as free cats, can hunt rats, which is very important in every city and especially in cities with warm climate. Killing rats by using poison is not "better way", it´s dangerous for the environment and even producing that poison itself is not good for the environment, people, etc.
Cats are natural hunters of rats and they should not be considered as ONLY pets, they are very useful for humanity, too, and they should be "allowed" to live ouside, as free, if they don´t have en owner and rescue groups didn´t find a "real home" for them. The overpopulation of rats, could be much more serious problem, than overpopulation of homeless cats, and that´s why cats should have the right to live their lives, even if they don´t have en "owner".
The using of TNR method (Trap-Neuter-Return) will reduce number of homeless cats and should be much more human for cats, people who work at animal shelters and many others. It is even much more better for the economy, environment, etc.