"Most people do think their used pet will be fine in a shelter."
Should read "Most people do not think their used pet will be fine in a shelter."
This is in relation to your thoughts about a guilt free surrender of a pet. You implied the shelters/rescuers provide a guilt free environment. My last paragraph addressed that. I hope that clears it up for you. I missed a word.
To have only shelters that will and do say no is removing sheltering. Once a no is heard, where is the animal going to end up?