"it's almost like "I win" button. Or rather cheat code. And other players still play the game, not knowing they have absolutely zero chances of winning."
I think you got straight into the heart of the matter. When known they won't break the game. When kept secret they are horribly broken.
This can be addressed by house rules requesting that anyone encountering such a site report its location to the game thread. This will actually serve to further spice up the game - imagine the pandemonium when all players learn the location of the "holy grail"
EDIT: All that said I'm still against removing the sites - well except maybe alt. as mentioned before - If we go the path of removing random mechanisms that dare to give some advantage then where would we end up?- Probably with an increasingly balanced & boring game.