I don't understand breeding dogs 'just because'. I also don't understand what you are inferring by this comment:
So because purebred dogs were developed for a specific purpose they aren't pets? Or we need to breed crossbreeds because they fill a gap that purebred can't fill?
Purebred dogs were developed for a purpose, and that purpose is what has led to the character and traits that make up the breed standard, the reason they still breed predictably even centuries later. Today, there are many reasons why purebred dogs continue to be bred, quite a few are still bred primarily for working ability. Many are bred for a combination of traits, and I don't know a single breed where breeders breed without aiming for the dog to be a suitable pet for the right person.
That's the great thing about purebred dogs, they fill a variety of purposes and tasks, including making great pets