Perhaps a possible answer if WW (and any other similar club) wants to keep itself as a pure flying club rather than as a public facility is to simply say that visiting pilots and their passengers are welcome to use the facilities. Most of those would obviously be visiting by air but I doubt if the number of pilots turning up by road would be a problem. If it were then a caveat that pilots using the club regularly when not flying in should take out social membership would seem not unreasonable.
When I do visit WW it normally is by air but I have occasionally dropped in there for lunch when I've happened to be in the area and as I'm a member of another flying club- where our aircraft is based- haven't felt that I was abusing the club's hospitality.