I wouldn't say TCC is THE great American Course, but it is "A" great American Course. If forced to answer which course is THE great American Course, I'd say there are 5-10-ish that make up a collection and I'd include TCC in it.
Before I go into more detail, let me just give the following background information. I last played TCC around 15 years ago, and in the late 80's and early 90s, I played TCC over 100 times. I'm one of a small group of people who aren't members but were very lucky to have access to playing the course on weekdays for 5 months-ish of the year.
One difficulty of evaluating the course is that if someone plays the Clyde and Squirrel nines as most guests do (and from the back tees as they are normally out), it is a medium-difficulty course. Even if one plays Primose the same day, I wouldn't say it's harder than most medium-difficulty courses. Playing the US Open Composite Course that they have now or the one for the Ryder Cup and the '88 Open is something totally different.
In fact, seeing what I've seen on TV Thur and Fri, it looks like the greens are medium in firmness and slightly soft and the course is also. I should caveat that 10 years ago, I thought the course was very soft, but that in the years after the '88 open, the greens were hard and firm, and the fairways were variable. One difficulty of controlling the firmness in the Fall and Spring was that it rained so often and winds could be fairly strong.
One point related to Paul Rudovsky's point about playoffs ... I've been texting some friends who are playing-in or part of the entourage of a player ... one point that I noted and mentioned is that TCC is a very difficult course to achieve separation as a leader, but one where a bunch of bogies can happen in a nano-second.
For example, on 11 (and the green looks much bigger than it did before) ... a shot a few feet away from the hole location toward the edge can easily trickle into rough that can lead to a bogey. On 14, Lingmerth hit two great shots and was about 60 ish yards away -- a great chance for birdie, suddenly became a bogey when he hit his wedge over the little ridge 10 feet past the hole and then putted 5 feet past on his birdie putt and missed the par putt. In the first round, Kevin Na was -3 after 5 holes and was +5 for the day two hours later.
On many holes, the key to scoring well is good defense. On the easy holes, birdies are great, but pars at worst are needed -- that being said, even the easy holes can be bogeyed.
I personally love TCC, but that could be because of a bias from my good fortune in getting to play it so many times. I do have a few friends who played Clyde and Squirrel and wonder how it can be a Top 10, or 20 or even 50 course. Again, Clyde, Squirrel, Primrose are very different from the course being played this week.