Enzo is a HYPERCAR, just like GT. get it right.
Hypercar never came into play until the Veyron was introduced, but even then, I still consider that a supercar in its own right.
In what category does the 612 fail to be a supercar then, other than it has more than two seats?
In a nicer way than Tor. said, it's not exactly an eye-grabbing Ferrari next to its F430 & 599 sisters. Look at what it took for the 599 to become really noticeable, even though it had mixed opinions.
You are just repeating that GT-R doesn't fit your definition of supercar. However it is fastest thing that has ever come out of Japan, hence why it IS a Japanese supercar, like it or not.
But it's still not a supercar anywhere else.
As I've said in the past, a supercar to me must be a car containing many things, not just performance. A supercar needs looks. It has to really grab your attention from anything else. Look at the S7, Enzo, or Carrera GT. They look absolutley nothing like any other car on the road, thus they stand out.
Supercars also usually put out abnormally high amounts of horsepower, horsepower that could be called excessive. Today's supercars push, 640, 660, 800, or even 1,000Hp from the factory.
They also don't need to be the fastest thing on the track. A supercar's performance is not judged by its lap time, but how bat-**** insane it feels to be behind the wheel. A GT-R can lap whatevere track in 2:04. An Enzo could lap in 2:06. What makes the Enzo the supercar though (when you're still mixing in the other elements of a supercar) is how it feels. GT-Rs have been repeatedly referred to as soul-less sports cars. The Enzo hasn't. Supercars will deliver their performance in a rush-driven experience. There's just something about them hauling around the track that makes the experience so much more...on the edge? It's like they have the ability to make their passengers cry for mercy. You have to do it yourself, but after running in a Gallardo & a LP640 at MSR, you know the difference. The LP640 is just so much more alive, so much more dangerous.
The last major component is typically how it's build. Hand-built is coincidentally a shared trait among supercars today. However, it takes more than that. The car has to have interior quality you'd never expect in a traditional car. The interiors of supercars just stand out. Today though, that's becoming a bit tricky to see considering many companies are now slightly re-redesigning interiors & and adding them to the next car. The quality of supercars is just there, though.
Lastly, supercars are generally the halo cars of a company.
However, it still needs to retain everything else from above.
And when you finally roll it all up, you get the last key trait of supercars. Price. Look at any car often recalled as a supercar in the last 7 years. What have they all held in common? A more-than-your-house-foo price. $300,000 seems to be the minimal these days, going up to your $440K Carrera GT, $600,000 S7 & Aero to your $800K CCX, & finally, your $1 million Veyron.
That's generally how I define it, though, and many seem to have a very similar opinion. But again, you can't have just 1 of these traits. You can't have just insane performance in a GT-R, incredible build quality like a Turbo, or just be a good halo car like the ZR1 for a brand. You gotta have it all. All of the traits combined is what makes a supercar usually called a supercar. And on the subject of the GT-R, it falls short. The design isn't eye grabbing in traffic like a Veyron might be. The interior quality, while good, is still considered sub-par by some. And the performance, while fast still has been noted by reporters as lacking soul, no excitement. When you see Clarkson's expression as he pushes a LP640 or a Carrera GT, that's the crazy, insane feeling a supercar delivers.
But, before you start calling any badge snobbery, it has nothing to do with that.
Any badge can build a supercar. It's how they execute the design, the adrenaline-feeling during a simple push of the accelerator, the quality, the craftsmanship of the car.
In the end, though, plain & simple. The GT-R simply isn't a supercar.