In fact, I predict that Cozart WILL improve substantially as a hitter at some point. Maybe not this year, but within the next 3-5 years.
I think he will follow in the footsteps of Ozzie Smith and make a major improvement in his hitting performance at some point.
If memory serves it is not that uncommon for a slick fielding SS who has shown to possess at least some of the tools at the plate to improve their hitting significantly with a few years experience with ML pitching. (ie Ozzie S, Barry L, and Davey C)