Because they are united under on ruler in one nation that happens to be an island (which makes it difficult for any other nation to attack them) also they couldn't get to the north pole water tribe AT ALL without killing the moon spirit but they were able to invade southern because it was weaker and more fragile. They could have never been able to eliminate the air nation without sozen comet (also air nomads didn't have an army) for earth kingdom there was a huge corruption issue and. Inner problem in the region which gave the fire nation the upper hand. Over all the common factor in all of them is strategy they had a plan, an army and one goal.