Using the right cartridges, within certain distances, and hitting the animal in the proper place they will take deer cleanly and humanely. So will a number of other handgun calibers. So, assuming you have a handgun with sufficient power and the proper bullets to take the type of animal you will be hunting, your own skill level is the place to begin when undertaking to hunt with handgun. Don't misunderstand me. It is never wrong to have a backup gun.
Mechanical things do break at the worst time.
But I have found that if you are hunting, carrying both a rifle and a pistol, and you happen to jump some game you will use what you have in your hand at the moment. Even hunting from a blind does not often allow a person the time to choose which gun they are going to use. They have no idea as to how to judge distances or where the vitals are located in the animals body and the shot placement needed to reach them from different angles. Some have never learned how to stalk game. I know that not everyone can afford to hunt big game all the time.