This is a subjective choice as those looking for a storage box for outdoor spaces can be very effective at keeping food and litter out of the cage from people passing by, pets escaping through windows, etc. However, if you are using a storage box without a lid, you can train your pet to draw their favorite toys from the box without any trouble or external help. This can give them a good practice of playing at their own will and will allow you to witness their independence. Another reason for purchasing an open basket is that it allows you to pile up the toys in one space.