I did and I jogged with them. the thing is, it's not just about the ankles strength but also it's symmetry form. biomechanics, foot type, etc... could also contribute with that. that is why I strongly disagree with certain shoe reviewers or self-professed experts that say otherwise that shoe cuts or height do not offer protection or minimize the chances of injuries. I'd take a foot /sports doctor advise over someone who has no idea or never considered those factors.
on the otherhand, I do sacrifice flexibility and agility when wearing mid/high cut shoes. although I feel much safer when wearing midcuts/high. I still roll my ankles but not as frequent as before. possibly because I'm less agile and slower now.