I dont know about im canada, but in houston animal control euthanizes the animals after like 2 weeks.
I think its better to let then try and make it in the woods or in a residential neighborhood than to give them to aninal control and have them killed outright.
Personally, I don't think euthanasia is a bad outcome for an unwanted pet. There are so many worse outcomes for a stray than a quick painless death.....animal abuse, neglect, starvation, etc. Its unbelievable what some people are capable of doing. So rather than take the chance of that happening, I'd rather have them taken to the pound even if you know they'll probably end up euthanized.
would you have a problem with someone using them for food?
No, so long as they are killed swiftly and humanely. I couldn't do it personally, but I realise that the distinction I make between dogs/cats and cows/chickens/pigs is entirely arbitrary