I've never had to take care of a crippled pet. My sister had her cat ran over my her uncle on her dad's side and our first dog was ran over our grandma who just threw him in the ditch. The closest I've had to taking care of a crippled dog was my grandpa's dog that he backed over with a tractor. She healed but she would hobble around the house and look so sad at not being able to go check on the cows with grandpa.
Personally, I think it depends on how crippled the pet ends up being after an accident. If it is a simple problem of getting a wheelchair so they can scoot around or a prosthetic leg, then it's a shame to put them to sleep. But if they are in physical or neurological chronic pain then I understand putting a pet down so it doesn't have to suffer anymore. But most of the time, it's just a lazy answer to a problem that needs a creative solution.