Another quick thought - imagine the situation with one tunnel (hopefully paired) between Europe/ America. And you thought LHR was crowded!!
Also there is a safety problem with Clarke's space elevator, as pointed out in Kim Stanley Robinson's Mars series; the cable is not in orbit and if anything break it then the result is catastrophic - much heavier/faster than the 'dinosaur killer' meteor (although the impact site would be a narrow strip around the equator)