RCZ

Your theory is kinda there, but your practical knowledge has some holes.

Yes, you will make more power with colder denser air. As air cools and compresses (think of a balloon after a few minutes of being in the freezer) you can fit more of it into the same space. This space being the engine. Denser air will contain more oxygen and will produce a stronger explosion in your cylinder per volume than warmer air will. That is why you get more power with colder air out of the same engine than you would with hot air. So far you are right.

Now in practice, the power difference between cold air and warm air is NOT by any means as huge as you are making it. You will never make up 5 psi from a turbo by feeding colder air into the engine. If this were the case you would see race cars with super cooled intake charges, not just intercoolers. So your theory of being able to run 5psi less with an intercooled engine vs a non intercooled engine to make the same power is way way off. In theory you could run less psi with an intercooler and make the same power, but the gains aren't really so huge.. if they were then those intercooler NX chillers would be huge. Some people also made ice boxes for intakes a while back to help cool down the charge, but you dont see those around much anymore do you?

Dont forget that there is also a pressure drop from using an intercooler. As in your turbo might be pushing 10 psi but your engine only sees 9 psi. Drops increase as the size of your intercooler increases so you will have to make your turbo work harder/hotter in order to reach the psi you want at the engine, which will negate the effects of the intercooler a little bit as well. Not to mention you will be running a BOV at this point, which means you will dump the pressure that's in your IC system which you will have to refill once you get back on the throttle. That little time it takes to refill ad re-pressurize decreases your cars responsiveness in on/off throttle situations and low rpm situations....which is to say the least annoying.

Now another misconception is that a turbocharger will make more power than a supercharger. That is NOT true. 5psi from a turbo is the same as 5psi from a supercharger, the power is the same. The only reason turbo kits make more power is because you can run bigger turbos with more volume and higher psi efficiency zones, whereas you are often limited to a lower max (efficiency speaking) psi with the supercharger.

As tardcore said, intercoolers are used to increase the safety of the system...to prevent charge air temps to be high and increase the likelihood of detonation. The best way to make a sc/tc safer is to have a nice efficient intercooler (big enough to cool, small enough for good response) and run some water or methanol injection in order to increase the octanage. That will minimize chances of detonation/knocking while getting the most out of your FI.