Every bear is a potential threat to a man, and so every encounter with a bear should be treated as if it could be deadly. (Keep your distance and be prepared.)
Is there any plausible evidence that once a bear kills a human it will usually change its behavior to include humans as preferred prey? If it does, then tracking it down and killing it would make some sense.
That is what I would really like to know, but I would prefer more than incidental or anecdotal evidence. I have read that the big cats have been known to do this in Africa and India. I have never heard from an authoritative source that bears have that tendency. It seems extremely improbable. Does anyone really know anything about this?
Such evidence may be hard to come by, simply because rangers do track down and kill bears that can be ID'd as having attacked humans. Usually, human remains are found in their stomachs. For this reason, repeated attacks are usually deterred. And outside the parks, humans are often armed and stop the initial attack.
In Africa and India, where man-earting cats have been known to have INDIVIDUALLY consumed literally hundreds of people before being shot, they were more elusive and few hunters pursued them with single-minded purpose until they could be encountered and shot. I think Jim Corbett, in particular, should have been knighted for his outstanding services in that regard. If you've never read his books, do. And find and read those by Kenneth Anderson, too.
One of the most chilling things that I've read was Anderson's account of stalking a black panther in the dark! He was so close to the cat as it approached him that he heard its lips pull back in a snarl and put a .405 bullet into it just in time.
I question your logic in thinking that it is extremely improbable that a bear that has killed a human won't do it again. I think the reverse is true, and problem bears in the parks have escalated their behavior. Such bears are usually tranquilized and moved, but some remain an increasing threat.
In today's social climate, I doubt that rangers would shoot a bear unless they felt that it would indeed remain a threat to humans. There'd be too much backlash from people like you and the PETA crowd.
If you have not read the books by Corbett and Anderson or the account of the Tsavo lions by Lt. Col. J.H. Patterson, V.C., I urge that you do. ("The Man-Eaters of Tsavo".) More recent attacks have been profiled by the late Peter H. Capstick, whom I knew slightly. His best single work on the subject is, "Maneaters." It discusses a number of species known to consume humans, including cannibals.
Anderson and others have commented that the Indian bears are very aggressive, too, and one of his books includes an encounter with one, as I recall.
