Allowing the cheese to melt fully into the broth can make it a little thicker and richer, and if the cheese melts on the noodles, it can give them a cheesy bite.
American cheese deliciously melts and blends with the broth, and mozzarella and parmesan also do well in the dish. However, avoid using cheddar, as it doesn't melt easily.
While cheesy ramen may sound strange, it's actually a common addition, particularly among Korean Americans, as some Korean dishes add cheese to mitigate the spiciness of the food.