This is because humans have specially selected non-aggressive animals, and many breeding routes for breeding beautiful breeds of animals have side effects in the form of health problems. Many domestic animals are not adapted to the wild, especially decorative ones - it will be difficult for them to survive in harsh conditions.
A cage and bondage is not a prerequisite for home keeping. It happens in different ways. You can almost not use any cages, leashes and other things. Walk / free the animal frequently. Many animals will return home on their own if you just pick them up and let them go.
Many animals get pleasure if the conditions of keeping the house are good - there is always food, nothing needs to be obtained, they also take care of you, pet, wash, treat you if you get sick. In addition, animals are direct in their reactions, if they are unhappy, this will be seen in their behavior. Many pets are very happy with their lives, if the owner is good. Living in the wild is a risk to life and health, a lot of stress, etc. The love of freedom is relevant, mainly, for wild animals, which already at a fairly adult age were taken to be kept in captivity.