well, think about it. is it easier to push a 5kg cinderblock on wheels up to a speed of x kph or a 50kg cinderblock on wheels up to the same x?
its the exact same with rocket engines, they just don't have as much of a problem with the mew (the coefficient of friction) because they are not...
instead of comparing it to ice, imagine it as instead going from water to gelatin to a solid form of gelatin. that's the best I can do to explain it without giving you a headache. you are correct with the fact that as it gets more compressed it would get warmer but the heat would radiate away...