I did some googling on these things and there seem to be more productive uses for them in space than as a means to reach space. It's pretty well understood how they would work in various uses but the engineering is the holdup. IIRC there have been several tether trials already carried out by NASA, one using the shuttle. Not much success so far but I'm betting my grandchildren will think they're pretty standard fare.
Like the 50's when they said the same thing about flying cars and the end of the internal combustion engine.