Getting that high has a couple of advantages: 1) You conserve fuel by following a specfiic flight path and it has the added benefit of also getting out of the

Getting that high has a couple of advantages: 1) You conserve fuel by following a specfiic flight path and it has the added benefit of also getting out of the atmosphere. The ballistic trajectory that they follow is the minimum-energy trajectory. Putting this another way, you maximise payload for a given amount of fuel, and so can deliver a bigger warhead for a given rocket. Additionally, why plough through half a sphere of air when you can get up and out? The advantage of their extreme range is that they escape the atmosphere and so don't deal with atmospheric drag the whole way. 2) Intercepting something coming down from above is far harder than intercepting something coming at you from down low, so it has that added benefit. I'm sure there's other advantages, but they're the ones that spring to mind immediately.