Exactly. They are close, and can sound good, but it's not the same at all.
Mathematically I should be president of the United States. In practice, I'm not.
Something "mathematically" being equivalent doesn't mean shit if sonically it is different man. Numbers don't mean anything when time and time again impulses can get picked out of a blind test amongst the real cab(s) very easily. That there is proof that the math doesn't mean shit. The SOUND is what matters, not the numbers. If somebody made a trashcan cabinet that sounded just like a Mesa 4x12, nobody would care about the math, they care that it sounds like the fucking Mesa 4x12 sonically.
See what we are saying?
~006
I think your problem is you don't understand the math in the first place, or aren't taking the effort to try to.
When these tests are being done, is it that someone positions a mic, captures an impulse, records a dry signal, and plays that through both the entire miced system, and also just through the amp and then applies the impulse response? Is the convolution plugin working right? I remember somebody posted something around here recently, and a bunch of convolution plugins aren't doing what they should be. Is the impulse being captured properly?
If something is different to your ears than the numbers are different too. If it sounds different, then its different, and that's either because of the reasons above, or because the system is not LTI. In either of those cases the math doesn't say that an impulse will work.
All I'm saying is, don't be so quick to reject the math. I'm not telling you your ears are wrong, I'm saying, if you hear a difference in a blind test, then there's more to it, and in particular there is a cause. If you did those tests and found you liked something better, there's a reason for it, and the thing to take away shouldn't just be a blanket "impulses always sound bad."
If you're trying to say that for a LTI system, you can hear a difference between the actual response and the stimulus convolved with an impulse (i.e. difference between a miced signal and a signal with an impulse applied, where the speakers do not distort), then that's totally unfounded. It's like saying that perpetual motion machines work or that gravity doesn't exist.
But if you're just saying that you can hear a difference, all I'm saying is maybe you should be aware that it's due to either a fault in methodology or the system is nonlinear, which it probably is. If it's nonlinear you shouldn't be expecting to get good results with an impulse. My point is, there's no divorce between the numbers and math, and what you hear, but rather that it's important to understand what that connection is and how to take advantage of it.
In your hypothetical trashcan sounds like a mesa 4x12 case, the math would agree! The impulse response of the trashcan would be the same as the 4x12!