I have played the course twice, and had two very different thoughts when I finished. The second time I enjoyed it much better because I hit the ball well enough to see some of the strategies and play to the greens from where the approaches were designed to be hit from.
First of all, the ambiance and history are off the charts. Yes, this says little about the course that is on the ground today, but it all plays at least a small part in the look and feeling of the place. The greens may not have been like that from the beginning, but I still see it as a cool classic look not found in many other places outside Scotland.
Secondly, the short game interest is off the charts. #2 does have in common with links golf that being on the green isn't always the perfect place to be, and there are often several ways to make a par from on or off the green (putt, bang a chip into the hill, pitch, etc.).
It's tough to discount the greens at #2 and look for strategy down the fairways. We all hope that C&C can restore a few angles, but what good are many strategic angles when the entire point at #2 is accurate iron play. Take away the greens and you have nothing unique at it stands right now. Add strategic angles to that and you have a flat course with strategic angles. I don't think the C&C work will be spellbinding strategically. The esthetics will be improved, and the unpredictability of an off-line shot to the wiregrass will be fixed.
People play (and pay for) #2 for a world-class test of iron and short game play. Those that have trouble will always say "what's the big deal? its a flat course with impossible greens." Those that can hit some of the shots (or can have a better attitude) will see it for what it is...one of the greatest short game courses in the country.