Feasibility of a skyhook - space elevator?

Leaving aside all the mechanics of the the thing (materials strength, differing orbital speeds at different altitudes, what the orbiting thing (which is not weightless) is going to pull against) there is the problem that you have this super strong lift line running across the orbits of hundreds of satellites - like all the GPS, surveillance and mapping ones - so it is going to be hit and they are going to be destroyed. Not good.