Well, the west has it's gnarly trails, too. I used to live in Boston and now live in Michigan and like to hike in the Southwest canyons. Lots of rocks. I switched from boots to trail runners a few years ago and loved it; made me a lot more nimble and my feet were a lot less tired at the end of the day. I've hiked the Grand Canyon a few times in Wildcats and recently switched to Montrail Bajadas.
Then, this past spring, I slipped, twisted and broke my ankle on the Tanner Trail in the Grand Canyon. I was wearing the Bajadas and carrying 29lb (day 1 descent of an 8-day hike, carrying 6+lb just in water.) Obviously, I don't know whether a stiffer, beefier shoe/boot would have made a difference but I've definitely thought about it and am inclined to think so. That said, there could very well be a bunch of accidents/wear and tear that didn't happen because I was more nimble in trail runners... Hard to say.
I'm 4.5 months into recovery and not back to backpacking yet. My first planned hike is in November and will be an "easy" hike compared to the GC. I expect to be in trail runners for that one. I still haven't decided what I'll do for my first hike back in the Canyon, hopefully next spring.