I can't see it as anything other than emotional extortion. It's not like the animal shelter is paying for that care. It's being written off, and the reason it's being written off is they make so much from the owners that do pay they can afford to do so.
It is NOT being written off. It is being paid for.
It wouldn’t make any sense otherwise. It would be a lose lose for an animal shelter to receive this deeply fragile animal and the vet to do this expensive surgery for free.
From a microeconomic perspective (which is also my own), I agree completely. I am trying to consider the macroeconomic perspective as well though, which quickly spirals into bankruptcy if they just start doing treatment for free for people who can't/won't pay for it. Unless/until we make it easier and cheaper for people to go to vet school, they have to make money.