The difference between a good punt and a bad punt will equate to approximately a 1st down. If you punt 5 times a game, then the difference between a good punter and a bad punter is about 5 first downs. A good punter makes a difference in a close game. If the game is not close, then it does not matter. A good place kicker is more important than a punter if you want to compare those 2. A kicker impacts field position with his kickoffs (which happen about 6 times a game), and there is a big difference between a reliable kicker who can consistently make FG's from 45 yards in, and a shaky kicker who is erratic and costs your team points. It could easily be a difference of 6 points in a game.
Special teams are the most overlooked part of the game. Over the course of a season, it will be the difference in many of the games. Even if it only swayed two games the difference between an 8-4 season and a 6-6 season is huge.