Those are benefits, but I think the main benefit of an intercooler is that it takes less energy to compress cool air than it does to compress hot air.

An engine gets all of its power from the power stroke, the other three strokes - intake, exhaust and especially compression - consume energy. With an intercooler, you have cooler air entering the cylinders, so the compression stroke uses less energy, leaving more power to go to the wheels.

This same principle is the reason behind using intercoolers on multi-stage air compressors.

Air-to-air intercoolers work on turbo- and supercharged engines because the compressor increases the intake air temperature and the ambient air is therefore cool enough to bring that temperature back down a bit. There might be some power and efficiency gains from cooling the intake air on a normally aspirated engine, but I doubt it can be done in a fashion that does not result in a net power loss.