First off note that this "allows", not "requires" shelters to put animals down sooner. My guess would be that most shelters know pretty quickly which animals have a chance of being adopted. Why make them waste money housing elderly, abandoned dogs just so they can be put down after six days instead of three when they can use that money to give better care to the adoptable animals. There are too many stray animals to all be adopted. Many will be put down. Period. They only alternatives are 1) Not allowing people to have pets in the first place, 2) Mandatory neutering. Take your pick.
Most of them charge for the adoptions, so they're not going to be in any hurry to put down something that someone will want.
I'm sure there will be shelters run by animal "rights" people that think it's better to put an animal down than have it live in "slavery", but your problem should be with them not with the gov.
People, put tags on your dogs and cats and don't let your snakes escape and you won't have to worry about whether someone else is willing to care for them...