The benefit of boots over shoes is ankle support. I hike with people that wear low cut Merrells, I wear Merrells as everyday gym shoes. I wear boots hiking because I have weak ankles, and it doesent take much for me to potentially hinder a hiking trip because I landed wrong on one or both ankles.
Wearing low cut shoes often can also benefit your ankles because the muscles in your lower legs build up reducing future ankle problems.
There are several exercises you can do to strengthen the areas around your ankles.
"Let's not miss the beauty of the forest by the ugliness of some of its trees." Bill W.