Purpose of flat response below 20Hz - Why does it matter?
I prefer to turn this question around.
Why on earth would it NOT matter to play what's on the disc?
It's always amusing to me to read the folks who say it's not important and their various reasonings for why that's the case, then to see that they don't have the capacity to play the first 2 or 3 octaves. I guess that's a pretty good reason to discount full BW playback in itself.

Would anyone here buy mains that roll off steeply at 5kHz and post why it's not important to have the last 2 octaves on the high end with a straight face?
There's no question of the importance of capturing everything that's sent to the SW output in my experience. But, I didn't stop there in asking the same question in the OP. I've set up exercises in which a scene is played with a steep roll off at 20 Hz, 18 Hz and 10 Hz vs letting her rip.
At 10 Hz and below, the consensus becomes more like 50/50, but anywhere above 10 Hz cutoff, it has been pretty much unanimous. Gender and age have no bearing on the results.
I recently posted this comparison from Hulk, the cop car bashing scene:

I also let people watch this scene from Terminator: Salvation with 20 Hz roll off and 3 Hz roll off:

Again, the result was unanimous; yes, there is a difference and yes, I liked the full BW presentation much better.
I'm in no way disparaging anyone's preference or subwoofer or opinions, just answering the OP, which is a question I've been asked countless times. It matters because a)it's what's on the disc and b)(according to me and nearly every person I've asked to listen and tell me if there is any difference and if so, which do you prefer) it adds a whole new dimension to the presentation.
Bosso