The reason that we must have the Commonwealth Games while we also have the Olympics is in order to keep up with tradition. While the Olympics have been around longer than the Commonwealth Games, both have been staged for decades and there certainly will be no stop in the commencement of these two events. The modern Olympic Games took place in 1896. The Commonwealth Games were first held in 1930.
Both of these international showcases have hosted some of the best Olympians to ever compete in the history of Olympic competition. The Commonwealth Games also acts as a warmup for the Commonwealth of Nations countries as they prepare for the regular Games. The Commonwealth Games are relevant to the athletes because they dedicate themselves and go through the training in order to be able to compete. There are looking to get on that major stage and show how much that their training has paid off.
There is a good reason as to why the Commonwealth Games take place regardless of the regular Olympics because it is tradition and it serves as a barometer for training Olympians.