I also remember J Goody saying she had her abnormal cells "burnt" several times before but they kept coming back.
The problem with burning (or freezing, really) the dysplasia is that you can't then do a biopsy and see if all of the affected area was taken out.
With LEEP, a cone shaped piece is cut out and sent for biopsy. If all outside surface of the cone is normal cells, then the entire dysplasia has been taken out and there is over 90% chance that it will not come back.
If you burn (or freeze) the area, it looks done but who knows if all abnormal cells were dealt with?