Why do this? If you do single long exposure, there is a very good chance your image will have an airplane fly through, a satellite streak by, or something more terrestrial like a fellow stargazer shining a laser through your frame, car headlights, etc. Taking a series of short exposures limits those issues, and if it happens, you throw out that shot and only loose 45-60 seconds instead of 15 minutes.
Stacking can also use shots you take when the lens is covered called dark frames. You take this for the same exposure time as the normal shots. This provides a noise pattern that builds up in any electronic sensor as the heat builds up from staying energized for so long (as well as natural summertime heat). That noise pattern can then be subtracted by the stacking software. The stacking software can also realign the images so you can use shots from multiple shoot days (er, nights).
Is it simply image quality? Or are there more trade offs?