Putting away toys also keeps them "new" to children. Kids can become bored with toys, even without playing with them, if they are in sight all the time.
SAFETY WATCH
If a storage chest is used, be sure it has a removable lid or a spring-loaded support that allows the lid to remain securely open. Also, check for smooth, finished edges, air holes to prevent suffocation and hinge-line clearances to prevent pinched fingers.
Other good options for storing and organizing toys are large, stackable plastic bins, smooth-edged baskets, or sturdy, open shelves.