One answer to this, at least, is that the multiple competing states allowed European civilization to flourish and to become powerful. This idea is proposed by, among others, Niall Ferguson in his Civilization: The West and the Rest.
According to this theory, competition brought out the best in these states. It forced them, for example, to keep up with one another in terms of the best ways to fight wars or to finance governments. If one of these states failed to adopt some advance in technology or organization, it could be overtaken by other states. This gave every state the incentive to push ahead as much as it could. This competition, then, made European civilization the most powerful in the world.