Why is standing more common on hills than on flats?
Because in the flats you reach higher speeds, and at those speeds aerodynamics become very important, so exposing more of your body to the wind is a drag.  The standing in flat is then limited to sprint bursts, or just used to give a little rest to your legs and buttock. Whereas going uphill is usually slow so the power advantage you may get standing is worth the trade-off for worse aerodynamics.