strong ankles through sneakers
When I hurt my ankle a few years ago, after two weeks I went to the doctor and he told me to keep moving. It took 3 months before I could hike up Monadnock.
I decided instead of getting stiff, ankle supporting boots I would get low super flexable sneakers. My idea was to make my foot as strong and supple as I could, and its working. Instead of climbing to the top of Monadnock or Wachusett on my training hikes I started to go horizontal and concencentrate on challenging foot placement on rocks rather than speed. I have lost some aerobic capacity ( didn't have much to begin with ), but my feet and ankles are more flexible and stronger than they have been my whole life.
An example of the change would be the steep slab of rock above the fan on huntington ravine trail. First two times I climbed it I was scared and nervous I would slip and fall. Three years of training with my sneakers I went back and climbed that section like a joke.
When I roll my ankle now its no big deal because when I train my ankle is in that position alot. I'm always trying to see how steep of an angle I can get on a rock, and if I slip no big deal because of the flex of my sneaker I always maintain some contact with the sole, not like a stiff boot where you catch an edge.