In the UK we don't have anything like day care services,at least not yet,but I have seen them on television with many more dogs than my pack of 4 and you are correct when you say they do not really know the dogs they walk.I agree with you about the cat,there is simply no valid comparison between a cat and a child.I will say that I do train my dogs to ignore cats quite successfully even when they are offleash:

http://i168.photobucket.com/albums/u165/bosscat69/Image0286_zpse9a3a3fa.jpg

http://i168.photobucket.com/albums/u165/bosscat69/Image0287_zpsc2d44c79.jpg

http://i168.photobucket.com/albums/u165/bosscat69/Image0288_zps26f9bf1f.jpg

I even train them to ignore pigeons which are often in the city center even if they are off leash :

http://youtu.be/VRrEPnCPWJw