Daryl:
A trap can be set and keeps working 24/7, with only occasional checking and rebaiting, whereas actual human pursuers would need to be paid, fed, organized in shifts, etc.
They would also need to be 'skilled' in the manner of Corbett so as not to add to the man-eater's tally! That requires training in tiger behaviour, stalking, marksmanship etc. and the up-keep of such training.

Also, although in this case it was actually trapped, I have noticed that Indians often use the word "caught" to mean "shot" with reference to a quarry animal that has been pursued for some time.