If the key is G you don't start with your hand on C and move it up to G, you start on G and move it relative to that root.
This matters because over/under moves usually happen at certain scale points. So if you learn the scale you have good chance of defaulting to the most efficient movements with muscle memory.
If you're referencing everything to C you'll never understand the scales and their different fingering patterns.
Anyway, here's Martha Argerich playing Prokofiev's Toccata. (What happens around 3:14 may be illegal. But here we are.)