This is gonna probably be a bad time, considering the influx of questions, but in Gold, Silver and Crystal, Blaine’s gym burns down, and it’s just him in that small cave (this won’t apply to HG/SS, where he had like a full gym, with puzzles and trainers.) Why do you think the Pokemon League let him stay as an official leader if it was just him in a cave?

Some of my speculation on the anime episodes regarding Blaine might be relevant: http://pokemaniacal.tumblr.com/post/28403196447/anime-time-episodes-58-and-59

In short, I think that because Blaine holds the rank of Gym Leader, and has given the League no reason to strip him of that rank, he has the inalienable right to run a Pokémon Gym in any area which currently lacks one.  He may even have access to a certain degree of League funding to assist in its upkeep (hence the more complete Seafoam Gym in Heart Gold and Soul Silver).