We had to let our pupper go a few weeks ago. The vet had to basically sit there and watch us while we processed the fact that we were about to pay her to kill our best friend.
For us, it was the worst day we had experienced in years. For her, it was Tuesday. She had other people waiting in the room next door, and had to go from solemn to bright and cheery over the span of ten footsteps, and she has to do that every day.
Her job is often to put a very real price tag on the life of a beloved companion. "I'm sorry, but keeping him alive will be $10,000... or we can humanely put him down for much, much less."
It's grim business. Necessary, but grim.
veterinarians are the most realists people in the medical field. While you put cost as the main factor my experience it is not simply a math problem, it is often a quality of life issue. Spending the $10,000 to extended a pets life for a another year is rarely about making the pet better, it is emotional support for the human companion of the pet while the pet will end up suffering for the year and die anyway.
So yes it is often cheaper to humanely put a pet down, it is often also the most ethical thing do to even if money was not a factor.
I call them realists because the face the inevitability of death head on in a way that we do not do in Human Medicine where we believe maximization of chronological age is the singular goal to be achieved at all costs with no regard to cost, pain, suffering or quality of life.
We finally found the right medications for my 10-year old loyal potato (she's had low thyroid function, immune system trouble caused by the low thyroid function, a rattlesnake bite on the nose, arthritis, and so on) -- she's now acting half her age and happily jumping on rocks to pose for treats, and it's so nice to share her story with the vet.
Everyone at the vet visibly brightens up when they interact with a happy well behaved dog.