I've heard this advice alot. My question is, why cover your break at
an intersection- what use does it do?

Suppose I enter an intersection with a green light at 30 mph (following
the usually defensive driving advice to slow down a bit), and I just happen
to see that pickup comming at me at 40 mph, running the red light. What
good will slamming on the brake do? Will my car really stop that fast?
Wouldn't it be better to slam on the accelerator (assuming my car could
accelerate that quickly?)

What's the proper "defensive driving" technique in that situation that
would make covering ones brake a good thing? I suppose- maybe, if you
stopped fast enough the pickup might catch you on the front end instead of
the midsection of the car. Any clues?