Well, no. Look, I didn't bring up country clubs or private clubs to start a whole new argument. I used them to show that not all establishments accept cash. In fact, some never accept cash at all. Now I sound like some kind of country club snob, when that is not the case at all.
Yacht clubs and country clubs -- private clubs in general -- operate for their members only. Your point is moot because if you do not belong to that club you would never be seated in that establishment in the first place unless you were with a member.
Now, if you are with a member, you would be seated but that member is responsible for the tab at that table. When the check comes it will not come to you. It will be given to the member who must sign for the lunch or dinner or drinks or whatever. His or her name is all that is required. In most cases, the server already knows the member and there is no discussion about the matter at all.
You may pay cash to the member who got you into the club in the first place in return for covering the tab, but that's about it. At least that is how I know these clubs work.