Saturn's rings are quite temporary on the time scale that planets exist at. They might only have been formed in a collision between moons 100 million years ago, and will most likely disappear in some 100 million years. This is a very brief period compared to the age of the planet.

So rings are likely quite an unstable formation, large moon or not, and we're lucky to have Saturn nearby right now. It is theorized that Earth used to have two moons that collided to form the current one and presumably also rings of debris that have since disappeared.