Pat:
Let's break the 12th down to its key components:
-a 8 or 9-iron par 3 (for most) with a green angled from left to right
-a central fronting bunker
-a tough recovery from behind the green
-the inability to bounce the ball into the green (whether due to a water hazard or otherwise)
There have been a slew of golf holes built since 1934 that have these attributes. Of those listed, some may come closer to matching these four components, but they are all at least variations on the theme. It is no secret that Nicklaus thinks the 12th is one of the toughest par 3's ever built, and has borrowed the concept in a few of his designs (including MV). It would not surprise me in the least if he had the hole in mind when coming up with the new 5th at PB or the 8th at Sebonack (TD may have a bit more information on this).
From the date of construction of the 4th at Deal, it is fairly evident that that hole was not the inspiration for the 12th. But MacKenzie had previously built several similar holes, so it is not hard to surmise that the 12th was not a novel concept in his mind when constructed. What I find interesting is that on a course where he tried to incorporate ground game options as much as possible, he built the 12th and the 15th, two holes where this option was entirely eliminated.
This leads to the penal nature of the 12th. As nerve-wracking as it is from 155 for the pros, it must be pure terror for a mid- to high- handicapper from 145. Its not a do or die hole like the 12th at Sawgrass, but it is a hole that requires a minimum carry. I have no doubt that the bulk of ANGC is a lot of fun to play from the Members Tees (and to answer your question I have not had the honor), but the 12th is not like the rest of the course in this regard. Not that there is anything inherently wrong in having one or two holes that provide a high level of challenge. But to say the course is clearly playable and enjoyable for all levels of golfers without pointing out that these types of holes are present is too simplistic of a statement. There's probably a great deal of enjoyment had by walking the same course that you've seen on television. There's also probably a great deal of fun in trying the shots that you've seen the pros hit, including at the 12th. It has to be a blast to hit and hold the 12th from 145 or 155 yards. But going to your bag to pull out another Titleist is probably no fun at all.
Here's a short list of replica courses built in the last 50 years:
Golden Ocala (1986)
Grand Cypress New Course (1988)
Cypresswood Tradition Course (1988)
Boyne Ross Memorial Course (1989)
Tour 18 Course (1992)
Royal Links (199)
Tribute at the Colony (2000)
World Tour Golf Links (1999)
Angel Park (1990)
Oakhurst (1998)
Sandhollow - The Links (2008)
Bear's Best (2002)
Renditions Golf Club (2002)
Wooden Sticks (2002?)
Just a guess, but the idea of replica courses coincided with the heights of the latest course construction bubble. With a ton of courses being built, the replica idea represented a niche market, giving the player the ability to experience many of the toughest, greatest and most widely known golf holes, including in some cases the 12th at Augusta. I look at it purely as a marketing ploy. Instead of building a new design, why not build holes that every player would want to experience but could not, whether due to access, cost or location.
To examine why these types of courses aren't being built with the frequency that they were in the 1980's and 90's is an exercise in examining the changes in the golf construction business in general. Call it the Keiser effect. There's been a steady paradigm shift from the glossy to the jagged, from high dollar projects to the found course. With minimalism being the buzzword of the day and the average builder of a course paying a bit more attention to the bottom line, we're seeing more Greywalls, Hidden Creeks and Steamsongs and fewer Shadow Creeks. Under the new model, the occasional Redan, Cape or Alps style hole does get built, but only where the qualities of those holes was already evident on the ground. I'd bet that if the components of the 12th at Augusta presented themselves on the right site, that style of hole would be built as well. With a few rare exceptions, the courses being built today are not being built as tournament course. Thus it is highly likely that any such "replica" would be a bit softer than the 12th at Augusta, a better fit for a course played regularly by members or paying customers.
One last point. When I was discussing the changes made in a replica that would make it more playable, I was specifically referring to replicas of the 12th at Augusta. I don't have the answer to this question, but I'd bet that the copies that have been built have features that make them a bit easier for the average player. Perhaps the recovery from behind is a bit easier, or there's a bit more room in the front for a miss. The point was that these holes are being built for the consumer golfer, not the professional. And they're probably being built to provide the 12th at Augusta experience, with a little less bite.