So the general consensus is that a shoe would have to have a 1/2" thick steel post in it to stop the forces associated with an ankle sprain. Since no shoe obviously does this, is what is there any benefit? Studies suggest the opposite...that high tops can't stop an ankle sprain but they do more or less slow down or delay your body's self-defense mechanism to an ankle roll:
High top shoes delay your body's reaction time to prevent ankle sprains:
https://jfootankleres.biomedcentral.com/articles/10.1186/1757-1146-7-14
High tops restrict range of motion but don't prevent sprains:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5721185/
High tops put more stress on the ankle area, particularly the Achilles tendon:
http://clok.uclan.ac.uk/16749/
You can find other studies showing no difference between low and high tops when it comes to number of ankle sprains. I just got my first pair of high top basketball shoes since I was a kid, and promptly went down with a bad rolled ankle that has kept me out the last two months. My bad.
I can tell you from those I coach and observe, people wearing high top hiking shoes roll their ankles far more.