A good grip will help your wrists activate in the golf swing correctly and will add power, distance and accuracy to your swing.
A tension filled grip, especially from having the shaft too much in your palms, will kill your entire swing. It stops your wrists from hinging naturally and then works its way up your arms and into your shoulders and locks up your entire swing.
Making mini swings with your elbows glued to your body will give you the correct sensation of the large torso muscles swinging the club, not the arms