That's no guarantee Ling Qi was capable of it, of course. I can easily see a situation where both of the more proactive solutions were beyond Ling Qi's means and required Liao Zhu to step in, despite Ling Qi making a good showing.
Look at it this way. Suppose Ling Qi could have succeeded in either choice; trying to pacify the spirit or trying to put down the spirit. Based on the new information that it's hopelessly corrupted and will have to be put down by someone to end its pain, then Ending it would have been the right choice of the two.
So if in a world where either choice could have succeeded, Ending it would have been right, then in a world where either choice would fail than you might at least have failed trying to do the more correct of the two options.