Mark,
If you're a club member in the UK and are coming to the states, you can have your pro write a letter or make a call and get you on all but a handful of courses, particularly if it's not in high season. If you wish to begrudge the fact that you have to pay a premium greens fee for this service, there are plenty of more reasonable public options available.
Amen again.
Mark - you don't understand the United States at all - and that's not a critique. I clearly don't understand the UK. If a private club were to open up its doors to the public, first, it could lose its non-for-profit status. Second, it would be legally tenuous for it to discriminate. While we can agree that discrimination based on color, creed, etc are bad, there's also good discrimination when attempting to keep a level of service, standards and conditions. In the US, a lot of these clubs aren't just golf clubs but there are social clubs and "homes away from homes" for many. Just as you likely don't invite ANYONE into your house, these clubs don't just invite anyone in as they are perceived as their homes (dinner locations, locations for their kids, recreation locations).
That's why, as Pat aptly points out and as I flippantly say, "put up or shut up", it's easier to accept members from other Clubs as they are theoretically "pre-vetted."
Finally, Dean, you're changing your tune more than the politicians in Washington. So now you're willing to pay a premium? My bet, you can get on most anywhere if you're willing to pay. There are outings at most Clubs (fundraisers by private parties) and anyone with a charitable bone has run across numerous opportunities to play most anywhere at a litany of charity events. So, is it that you want and think you deserve access or cheap access?
I'm sorry to say this but nobody on this board wants the average American showing up at any of their private clubs to play on a daily/weekly/monthly or even yearly basis. Pat has said so much in his own way and I tend to agree.
And I haven't even gotten into the financing ramifications. Many seem to think the greens fees makes up for the individuals "club footprint" that day. This isn't even close to true. What does it cost to staff a course for play, to pay of the massive clubhouses, the staff, the tax bill, the pool, the gun club, the holiday events, the management, the inventory, the merchandise, the driving range, the carts, the equipment, the HVAC upkeep, etc.....all to make that guest a "member" for one day. US Clubs don't have the benefit of an extra 200 years of payments and are burdened with labor issues, tax issues and expectations a whole lot different than what's going on in the UK.
If you're going to merely look at the greens fee and ignore the other factors that go into a round of golf and a "member for a day" experience, I paid around $1,600.00 per round of golf this year at my club.