"With high-tops and appropriate lacing you are better protected from rolling your ankle."

Your ankle is supposed to twist & roll. The number of muscles & tendons in your foot+ankle dwarfs those in your knees/hips by many orders of magnitude. Properly conditioned, they all work in unison to keep you steady and "sure footed".

If you isolate your ankle/foot in a cast (ie boot), guess where twists & rolls are transferred? That's right, but your knee isn't supposed to twist - it's just a straight lever.

Here's a good conceptual model: your hand/wrist becomes tired from some kind of activity. Rather than spend time strengthening your hand/wrist muscles to perform the task(s) as required, you decide to lock it down in a rigid glove/cast, transferring all the kinetic energy to your elbow & shoulder.

Now, who would ever consider doing something like that? Well, the same is true with a barefoot/minimal approach vs boots. But the process isn't easy for "zoo humans". We've been wearing shoes with heels/ankle support for so long that it takes a very long time to condition your foot to the point where it operates as it should in nature.

To give you a specific example: me. It took me two years of jogging in 4mm rise minimal trail runners before I felt confident enough that I could barefoot run (on semi-packed dirt). And even then, it's a modest proposition; day-in, day-out, I use my trail runners.

The modern day bible that describes how humans walked & ran for 2m years - up until 30 years ago - is:
http://www.amazon.com/Born-Run-Hidden-Superathletes-Greatest/dp/0307279189

Here's a quick recap:
https://www.youtube.com/watch?v=2JWUhW5yRdI

Here's a medical overview of how our feet & legs are suppose to operate:
https://www.youtube.com/watch?v=zSIDRHUWlVo