I shall have to bow to Lu's superior knowledge of current technology.
But I believe the point that was being made was that once constructed the Space Elevator is a (relatively)stable system, hence the only only problem is how to build it. That I suspect will be a problem for our grandchildrens' grandchildren. Just because we can't figure out how to build it now, doesn't mean we won't in the future.
Got to admit that it is an elegant solution for access to orbit though, and indeed furthur exploration/expansion through the solar system.
w.r.t. the energy problem, all problems dissapear if you send up as much mass as you bring down. Then you are only dealing with frictional losses.
p.s. by the last chapter (set several hundered years ahead) they've got four, sited around the equator, then linked them up with a ring.
and lets not even get started on Dyson spheres, or Niven rings