I do agree that it's heartless. However, speaking as an ex-Zoning Officer, the problem is that people who put up signs like that never bother to take them back down. Same with yard sale signs and such. (And while I'm the first to admit you shouldn't compare "Lost Pet" signs to yard sale signs, well, a sign is a sign is a sign. Sorry.)
That's where the trouble really begins. My job was to talk to people who put up all kinds of signs like that....they had to take them down or I would. People put signs up on utility poles, public trees, whatever they can find. They nail them fast to the poles or to the trees. And, yes, unfortunately, it is against the law. And one can be fined.
I was always more understanding about lost pet signs because I know how hard it is to have an indoor kitty or dog become lost. And I caught some flak from municipal officials because of it.
You have to realize, too, that a lot of businesses (big sign companies, for example) will look for any loophole whatsoever in a zoning ordinance. And then, if they find something, they can take the municipality to court and have the entire ordinance struck down. And believe me, it's been done. So if you do allow "Lost Pet" signs, it can be considered discrimination.
Stupid, but true. With zoning, there are few areas of grey.