We bake like that because it's the only way we're taught, LOL! Just like you're taught metric and weights.
Try these:
http://www.joyofbaking.com/USMetricVolumeEquiv.html
http://www.joyofbaking.com/USMetricWeightEquiv.html
I would be careful of using the weights though. The volumes are more accurate than the weights because of exactly what you mentioned. 1 cup of flour weighs less than 1 cup of sugar, etc.