Aight, lets take a look at a very common situation at a regular racetrack.
Here is Sepang Circuit:
See those turns at the end of the straights? You're gonna be going down those straights very close to the redline while cycling through the gears, at which time you may be travelling at a better than average pace[to say the least] If you apply the technique that Cav has suggested and use the engine brake to slow the car, you will still have a longer overall braking/slowing distance than a driver who is approaching the corner on his brakes and downshifting as per the usual methods.
Congratulations, you have been out-braked.
If the engine brake is applied too severely and you cycle down through the gears too quickly the wheel speed will plummet as soon as you dump the clutch.
Congratulations again, you have spun out.
If somehow you manage to keep the wheels in traction and still be ahead of the other guy, you'll enter the turn and exit at a gear too low; going back to 2nd was necessary to slow the car for a 3rd gear turn, and on the exit you're gonna have to build the revs again in order to get to third and then to fourth while the other guy has already topped out his revs on the exit and is already midway through his powerband in 4th and going for 5th, if not 6th. This of course takes for granted that both cars are identical.
Happy, happy, joy, joy. You were out of gear for the corner exit and will now have to play the late-brake game to catch the guy in front of you.
Hope that helped guys, Cav this was not meant as an attack on you in any way, and if it sounded like one, I apologise unreservedly. Jus seems to be the most efective way of getting the message across.