First off they can run, climb, swim, fish and fight.
Wouldn't they be very useful? It seems to me that bears are the most intelligent of the three because of their resourcefulness. Couldn't they be 'guard bears' or retrieve things? Surely they would've been good in battle. Bears are more similar to humans than cats and dogs, being omnivores; this would also make them easier to feed. I once read that eating fish was one of the main ways that humans became so intelligent (I have a absolutely no source) so maybe this means that bears have some extra intelligence too.
When I've posed this question to people in person, a common response is that "bears are solitary, unlike dogs" but then so are cats and they were domesticated just fine. Another problem might be that bears hibernate but this could've been worked around or bred out?
We likely didn't domesticate dogs and cats. Dogs and cats likely domesticated themselves. Human populations create a lot of food refuse that dogs and cats can scavenge and attracts other animals that dogs and cats can prey on. The animals that expressed less fear and hostility towards humans were more likely to succeed because of this, and eventually they became integrated with our societies.
Bears, being significantly larger than dogs and cats, can't survive off of scraps. No mechanism exists by which they could easily be domesticated, and we haven't been advanced enough to capture bears for a long enough time to breed them into domestication.
Also, that factoid about humans and fish is almost certainly false. If anything, what allowed our brains to grow so rapidly was access to bone marrow scavenged from the kills of larger predators, as getting at the marrow is significantly easier when one has simple tools.