These are some reasons I found on the web, from a certified trainer, which explain quite clearly the importance of using a crate with a young dog.
1) Puppies can be very tiresome to adult dogs. Keeping the two of them separate while you are gone will most likely give your older dog some much needed rest.
2) I'm going to assume that your adult dog is bigger than your pup. Even in play, there is the chance that the adult dog can injure the pup. I wouldn't take the chance of you not being there if it happens.
3) Puppies need around 18hrs of sleep a day. If there is another dog to play with and things to run around and do, the puppy will be less likely to sleep and can therefore be cranky just like an overtired child. Sometimes they become overstimulated and tired, which leads to increased nipping behavior.
4) Puppies put everything in their mouths and chew on stuff. As a vet tech, I assisted in many surgeries to remove objects from the bellies of dogs. Not all of these dogs survived and if they did, the owners paid thousands of dollars for their surgery and after-care.
5) Each time your puppy chews on things that it is not supposed to, it teaches the puppy that it is ok to chew on those things. Crates keep puppies from practicing unwanted behavior.
6) It's no fun coming home to chewed stuff.
7) Puppies have an instinctual urge to not soil their living space. By crating your puppy, your puppy will learn to "hold it". If your puppy is roaming around, there are lots of opportunities to potty and walk away from it. Each time your puppy has the opportunity to potty in the house, it allows your puppy to practice the behavior and teaches the puppy that going in the house is ok.
Here is an article on housetraining: http://www.k9clicking.com/
Here are two on crate training: http://www.clickertraining