In comparable situations, Shatner's Kirk always used stun setting through and through, though. You can't interrogate the victim of kill setting, but there's no similar disadvantage to spraying everybody with the heavy stun setting, assuming the effect keeps the victims down for at least a couple of minutes.
In STXI, Kirk and Spock really only appeared to have a tactical need for stun: to capture a source of intel, and then to plow routes to Captain Pike and to the supply of red matter. Kill provided no obvious advantage...
...Unless we assume stun is unreliable and frequently fails to down the target on the first or even the third shot. Which is quite possible, as in many other situations Kirk was in a position to take an ideal shot (thus ensuring downing at first shot against odds), rather than engage in a complex firefight where all shots were unideal as in STXI.