snip

BTW, a few years ago I heard of plans for a network of Low-Earth Orbit
satellites, that would avoid this problem. I wonder what happened to
that?

snip

check here

http://en.wikipedia.org/wiki/Teledesic

I suspect the project died because it still had excessive latency,
especially since they had to add an "internal" protocol to the
network because the LEOs are not stationary in the sky. (never
mind the *astronomical* cost(pun intended))