I can see how alternating the over/under grip would help maintaining symmetrical grip strength, but not sure how much crossover there will be to other exercises that require a high degree of grip strength.
Essentially all an over/under grip style does for the lifter is increase grip leverage, but is not as effective as increasing grip strength via pulling on a barbell with an overhand grip sans the hook grip.
The over/under grip style(powerlifting grip) is a cheat grip. It helps keep the bar from slipping out of the lifters hands, but the strength crossover to other grip related exercises won't be as effective as an overhand grip.
Originally Posted by Ben Moskowitz
According to Jlascek over on Strength Mill
food for thought