Pets don't really need medical care per se. There's a huge glut of unwanted dogs, so is it better to euthanize so many unwanted dogs right away, or would it be

Pets don't really need medical care per se. There's a huge glut of unwanted dogs, so is it better to euthanize so many unwanted dogs right away, or would it be better to just allow some of them to live on the street with homeless people, and then be euthanized when they have medical problems (which usually takes years: pets are typically fairly healthy until they get older unless they get injured, much like humans)?