Then you have an enormously large tower held up by nothing but its own strength instead of being naturally pulled into space. Also takes additional delta-v to get satteliges into common orbits post release.
This is arguably more doable than cables. I've been told that it's completely possible to build steel structures several miles tall (and the main reason we don't is b/c elevators become a problem).
No known material could support a tower that tall (towers need compressive strength; elevators need tensile strength). It would need to rely on 'active support' or 'dynamic structures', like a space fountain ( http://www.orbitalvector.com/Orbital%20Travel/Space%20Founta... )
A friend of mine who studies engineering told me that masonry has infinite compressive strength meaning, in theory, it's possible to build monumental structures out of stone.