Don't tennis players cut just as much, if not more, than basketball players...and they use low tops pretty exclusively. I never really understood this ankle support thing. Maybe it is actually in reverse, Haymitch. Maybe it is actually for the slow, lumbering Bigs who are awkward, versus needed for ppl with fast lateral movement and making cuts like Micheal Chang.
I play in Kobes... they flare out the sole which I think provides better ankle stability. My daughter plays point in HS ball and has played the last three years in Nike Hyperchases (Hardens old model) and she doesn't even use the ankle braces anymore. A Select club she played for tried to have her wear a team shoe (don't know the Nike model, my daughter called them "bowling shoes") and she stayed with her lows. Its mostly what you are used to...
tennis players dont need to change direction to the extent of basketball players or worry about stepping on other people's foot. Tennis is generally side to side and straight motion in pretty much a wide open area
i always wear lowtops.....most nike/jordan's the past 15yrs have had anti-roll features built into the heel and outer side of the soles.....you can even test them, trying to roll your ankle on the outer edges is impossible
Like others have said, just depends on what you feel most comfortable playing in and how you play. I've worn lowtops(Kobes) and high-tops(Hyperdunks) and I've rolled my ankle in both. So yes, my answer didn't help.
I'd never wear low tops, it would be a blessing if i didn't roll my ankle every game.. Saying that, high tops are so restrictive and don't feel natural to move in at all. The best is and always will be mids imo. The Tmac range were glorious in their comfort and stability and i've since moved to the Rose range which are equally if not more comfortable and supportive. I think you already know the best answer is mids but if it's just a low key pickup game and you're a post player, wear tennis shoes or runners.