I saw a great talk on PBS by Burt Rutan where someone from Florida asked him that very question. Sadly I can't find it on YouTube. He said he could never operate out of a government-run spaceport because the red tape and bureaucracy would never let him get anything done. He has tried it before at Vandenburg in California and he finds it cheaper to build a brand new private spaceport from scratch than to try to operate at a government-run facility.