I live in a small town. I grew up being a "dog" person, but now I guess I'm a "cat" person as feral cats seem to find their way to my house and I have a soft spot in my heart for all animals. (All cats that stay here get fixed, by the way). When one of my cats get sick I take them to the vet here, an old fashioned country vet who does things the old fashioned way, and he will give them a shot and usually the cat gets well.
But, a few years ago I moved back into the city and took my cats with me. It was my experience in the city that if you take a cat to a city vet, first thing they ask you is "where you got the cat". When you tell them that the cat just found its way to your home, unless you are willing to give them a blank check to save the cat at any cost, they will pressure you to put the cat to sleep. I guess this is just their way of dealing with the cat over-population.
After moving back to the small town, I mentioned this to the country vet here, and while not wanting to speak negatively of those in his profession, he basically confirmed my suspicions. Many vets would just rather put a cat to sleep than try to heal them, unless, like I said, you are willing to pay thousands of dollars with no guarantee of them getting better.