Not so much contests, it's just with a shorter flying season, there are only so many weekends for TAG, fly-ins and fun flys, pancake breakfasts and club picnics, etc.  Along with community building, special events (Veterans Fly-in, Cub Scout groups, aviation camps) along with associated back up dates, because invariably ole Mother Nature puts a damper on a few things as well.

All the clubs around here make it work, there are enough full members of multiple clubs that things don't clash too much.  Other than the short flying season (compared to y'all in the South) I feel very fortunate to be in an area where all the clubs are great and are able to work with each other.

As the OP asked, I think that all clubs could benefit from an "Associate" membership (as long  as they are a full member at another club and an AMA member).  It fits the "just fly" crowd and generally avoids the situation of asking a "guest flyer" that since he or she has flown X amount of times at the field that they need to pay full dues.