I actually didn't think about that, but that is incredibly true. My reasoning is that there are obviously more than three schools in Britain and especially in the world.
You may recall that both Karkaroff and Madame Maxime were extremely upset that Hogwarts ended up with two champions, and that, combined with the events that led to Cedric's death, may have convinced them, or at least their respective boards of directors, that it was not worth the risk to their students. It may be their only chance to hold another tournament to appeal to the headmasters of other schools.
As for what other countries...use your imagination. If you want to use an Australian school, use one. If you want a Brazilian school, use one. It almost gives you carte blance to explore different cultures and how they might incorporate magic into their societies.