Well, I may be barking mad here (and I'm counting on you guys to point that out if I am), but here's a reason to use Aqua Velva (or any other alcohol based AS):

Use it to help tune your technique. Say you've just finished shaving and your face feels BBS. You think "awesome." You splash on some AV and your face is on fire! So, you may have achieved BBS, but your technique isn't quite there - angle too steep, too much pressure etc = razor burn.

Another scenario: You've finished shaving and there's still a fair amount of stubble. You splash the AV and no pain whatsoever. So then, you could be a bit more aggressive next time - increase blade angle, use a bit more pressure or work on ATG.

Of course there are many other scenarios in between these two that can help you refine your technique. So, when you splash on the AV, pay attention to where it stings (or doesn't) and how much. It may help you refine your technique.

Oh, and BTW, make sure you use a nice moisturizing AS after the AV - your skin will love you for it.