Sean Arble & Glenn
American clubs are subject to American laws.
Our legal system differs from that of the UK
As to the issue of spectators, at the Crump, Anderson, or any other tournament, you can't ignore the issue of liability.
As a club member, would you want to expose yourself to the financial risk inherent in having non-members roaming the property.
At special events, be they in Madison Square Garden or at a U.S. Open, when you purchase a ticket, in most cases you waive legal liability against the host/sponsor, including the owner/promoter of the facility and event.
That doesn't happen when you open your doors to the public.
I'm not saying that the issue can't be resolved, only that there's a lot more involved than you think, including risks. And, most clubs don't want that involvement, there's very little upside to it.