The worst part of playing one course repeatedly is that you hone a set of skills for only that type of course. When you wind up playing courses outside your comfort zone, it gets difficult. For example, playing links courses demands an ability to hit lower shots because you are playing into winds. Playing the wide open and long courses demands distance far more than accuracy.
Additionally it stops challenging you in strategy because after 5 or 6 rounds of the same course, you will settle on a strategy that suits a hole and course and tend to stick to it