It doesn't necessarily directly starve the other dogs, they'll have less energy to attempt to reproduce with. It's not an attempt to increase the death rate as much as it is an attempt to decrease the birth rate.

My "also, wtf" stands.

This is exactly why stray dogs shouldn't be allowed to exist. They're a threat to the community. We don't have them at all here in Japan, as far as I can tell; we do have real wild animals, like bears and boars, that sometimes threaten and attack people, but that's normally only in rural places, and those are actual wild animals, not feral pets or invasive species. We also have stray cats, but while one might argue those are a threat to some native animal species like birds, they're certainly not a threat to humans.

Who funds the shelter system, and where do the dogs end up?

It's hard for a small municipality with a stray problem to justify a facility that is entirely dedicated to the bureaucracy of scheduled death. This is a tale as old as time and the end result is not a happy one.

The term "kill shelter" is much more common than "shelter" because by nature a shelter is temporary housing before euthanization resources are available/confirmed.

Read my sibling reply from 3 hours before yours: https://news.ycombinator.com/item?id=38175512

The populations will just rebound unless you really manage to euthanize all of them. Sterilizing and vaccinating takes care of the problem.

Unless the problem really got out of hand, it's not just "some people" who oppose a total cull. Even if people silently approve of the cull, one will find much less volunteers for such an effort than for a large-scale sterilization and vaccination program.