Stop euthanizing animals

PETA says that in the U.S.A. alone four million dogs find their way into a "shelter" every year, and I am persuaded that even more cats find their way there. 
Euthanasia as I understand it should apply to people begging to die, not animals begging to frolic till the cows come home.  Why can shelters not bring their shots up to date and release them?  The dangers to the public are greatly exaggerated, and the dangers to the animals are far greater.  There are no dog catchers in India and they are not killed (or eaten); people feed their neighborhood strays.  Can we do less?  I guess we can -- a lot less. 
Is this to placate people who hate animals;  who stepped in some poopoo on the beach; whose solution is to kill or ban all animals not on a leash?
http://www.youtube.com/watch?v=Rcm8tTkEGsI&feature=related
The benefits to society would be far greater if people were not allowed to walk on the beach without looking where they are going.  Thousands of years ago we invited dogs and cats to live among us, to live with us.  They are living up to their end of the bargain, or trying to with all that is in them.