The main reasons I wear lightweight mid top hikers is they protect my ankles a bit from scrapes on rocks and branches, keep them from getting pierced with thorns, and they keep out debris better.

Of those 3 reasons keeping out debris is by far what they do most. I can't take two steps in low cut hikers without picking up rocks and twigs and other debris, even when I'm on a dirt smooth trail.

But really, I just prefer them. I've never liked having my ankles exposed while hiking or working. It really is a personal preference thing. We can tell you why we use what we use, but in the end you have to figure it out for yourself.

One thing I think most of us would agree on is that the insoles in most shoes today are pretty crappy. Wondering_Daisy pointed out she uses "SuperFeet" insoles, and I've heard a lot of others recommend those too. The main point though is you might want to buy good insoles first and bring them when you go look for shoes.
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"You want to go where?"