...On Pro Shops

Your Pro Shop is for marketing – period. 

Every member should have a logo’d bag. Every member should have a wardrobe of logo’d apparel. They should drink from club logo’d pilsner glasses and carry their luggage in nice leather bags with the club logo prominently displayed. 

You already spend next to nothing on marketing anyway. Let your members be your walking billboards. Just make sure the price is right. It’s not the money you make on each piece, but the consistent image and reminder you are putting out to people that aren’t yet members.

...on Private Carts

You want a billboard to potential members that says, ‘the inmates run the asylum’?

Keep allowing private carts.

The members that will fight for them are the very ones keeping new members that would actually spend money at the club from joining.