Cats don't always die. There are several mystery series where cats are the detective's pets and continue on from novel to novel to help solve crimes. "That Darn Cat" was an FBI agent, who survived, as I recalled.  And there is a very strange but rather fascinating vampire movie where the cats save the day against a particular vicious mother-son duo. 

Cats get rather a bad rap because they aren't dogs; but that's also why cat lovers adore their felines.  In a story, you might get a very different emotional response from an audience who discovers the detectives pet is a tarantula rather than cat; and the death of a rat might be less emotinally wrenching than the death of a puppy to some people. But a pet, whatever it is, does show an ability to love and attach emotionally to something outside of the mirror, and that may be the strongerst reason for allowing a charcter to have that connection.

 I find stories / movies / television shows that have no animals in them to have no reality. The difficulty is with dealing with the pet when you need to let your character move around (your hero can't abandon a dog for a week to follow a case unless you want your hero to be arrested for animal cruelty), but how he or she handles the responsibility can make the audience sympathize or become disenchanted with the character. 

The problem is the same one as having a child or another dependent involved in the life of the hero.  It is easier if everyone is beautiful and young and healthy; but there is not a thread of reality in such a story, and, frankly, I lose interest fairly quickly if no one has responsibilities outside of the plot line. 

Every wonder what people work at in movies and television to be able to afford pent house apartments?  How do they hold a job that apparently that has impossibly flexible hours? Ever wonder how emotional remote they must be to have a different lover every week, and no real family, and no relationship with any living creature except "friends" as shallow as themselves?  Boring, boring, boring.

I read a somewhat mystery recently about a man and the dog whose speech he could understand but no one else could. The man was a yawn---a creepy gambler who managed to bed gorgeous women for no good reason than he was the main character.  The dog was funny and insightful, and I wish the novel had been about him instead.

And the dog did survive, by the way.