I can't think of a single army in the world that has its soldiers not wearing boots. In the US Army I never had a rolled ankle, but most certainly would have had I worn trail runners.
Light pack or day pack and well established trail? Maybe trail runners are superior.
Then again, there are not a whole lot of through hikers on the PCT that hike in boots. Given the fact that these folks can make that choice (vs people in the armed forces), this says something. Let’s face it. Most people find that hiking miles and miles in boots just, well, sucks. Especially if you have to do it day after day. Of course, at the end of the day, it all comes down to personal preference.