Do you think that dogs and cats are useless eaters?

I wouldn't say that, one of my cats woke me one night to warn me that a stranger was outside my window in the middle of the night trying to look into my bedroom. Another cat warned my family that the chimney was on fire. When I was attacked by two large dogs, my dog came and scared them off. They all deserve every meal I gave them.

Many dogs do all kinds of work. 

I do not think so. They provide companionship to their owners.

Not at all. Pets perform a vitally important role as friends and companions. 

I don't have pets because I want them to do work. I have them because I enjoy their company.