I concur with using low top trail shoes when possible and doing exercises that keep ankles strong and general fitness high. Look up proprioreception exercises. I used to occassionally sprain my ankle about a decade ago as I first transitioned into trail running, but that stopped with time on trail and various agility exercises. Time in class 2 terrain helps with agility and strength as well. I broke my ankle two years ago when I made a bad decision with a poorly balanced boulder, but would have done so regardless of footwear. The good news is I learned even more proprioreception, leg strength, and core exercises, and became more disciplined about doing them consistently. My ankle may never quite be 100% post-injury & surgery, but after rehab, training, and shedding a bit of weight, I now hike farther, with better balance, and with no ankle sprain or other issues like I had when I first became a trail running and endurance hiking enthusiast.
I actually wished I had worn trail runners on Shasta last weekend. I got nasty heel blisters wearing boots I hadn't worn for 2-3 years. Unless conditions are extremely cold, highly technical involving extensive crampon use, or I am at high risk of being out in wet cold overnight, trail runners and extra socks are my preferred footwear. Plus, I can usually pick up high quality pairs of La Sportiva, Montrail, etc. trail running shoes at Sierra Trading Post for $30-$50 per pair with online coupon deals.