What if the animal is raised in captivity? Wouldn't they be domesticated and thus less of a threat?

Absolutely not.  Just because an animal has been raised in captivity or even bred through captivity for generations, DOES NOT mean that it is domesticated.  Domestication takes thousands of years of selective breading; in other words; it is a very long process.  Although the cub/baby animal may seem docile, it will grow to be many times its size and very powerful.  As it grows into adulthood, you will see some of the more aggressive tones arise in its personality.  This animal evolved in the wild for thousands of years, adapting to be able to survive and hunt in their natural environments.  It has inborn instincts and behavior patterns that cannot be erased.  A 300 lb. lion can easily take down an 800 lb. water buffalo with one swipe of its powerful paw... so what could it do with a 180 lb. man?  A 70 lb. child?  

Aside from physical power posing a danger, many animals were brought from outside the country.  This means they could be carrying diseases that you're not immune to.  These Zoonotic diseases are very dangerous (like the Monkeypox outbreak in 2005), and can be transfered to humans and native animals, which can pose a danger to the eco-system by wiping out some of the native animals and disrupting the food chain.  

Monkeys are HUGE problems when it comes to diseases.  They can carry Monkeypox (I'm not joking), Herpes B, and many others.  

Not only are they dangerous, the cost to take care of them is sky high!!!  Proper facilities, food, cleaning, care.  Just to feed a lion, it would cost you $80,000+ annually!