there wouldn't be to much swaying, as any attempt would already put said line under an even greater tension, assuming it can handle it, the resulting wave produced by swaying would be quite powerful, and anything on the line would probably be thrown off. plus swaying woudl involve chaning the orbit of a specfic section of the cable, somthing that takes a lot of energy. for example, launching a satelite into a into an equatorial orbit then chaniging its inclination to 60deg takes as much energy as it took to get it into orbit in the first place. of course thats just one small problem in a mess of others. assuming all of them are solved and we don't find a cheaper way into space it will work just fine