Bears are a great capture in the early game, especially when you want that culture boost to your new city before you can build a Monument.
However, after you get a Bear for each city to entertain the populace, the map is loaded with them. I know it depends a lot on the size/type of map you use, but I find in all my games there is a bear explosion.
I was thinking that having so many Bears prevented the other barbs from spawning and I was seeing very few Lizardmen, Wolf Riders, Axemen, etc. So, as an experiment I went into the World Builder and deleted 159 Bears. There were still plenty on the map. I thought this would bring a real raging barbarian event, but I was wrong. In just about 50 turns all the Bears were back.
I'd like to see something in the game that would slow down their spawning. Even if the other types of animals cannot be increased at least the real barbs shouldn't be prevented by spawning by so many Bears. It is just another reason why the raging barb option doesn't work beyond the early game most of the time IMO.