First of all, AGNs and QSOs are very energetic, often hundreds or thousands of times more luminous than any other galaxies in the universe. That means that they have a substantial influence on what goes on in their vicinity of the cosmos.

QSOs, for example, may have played an extremely important part in the history of the universe some twelve billion years ago by ionizing (and thus rendering transparent) much of the obscuring interstellar gas spread throughout the cosmos at that time. Without this crucial ionization process, we would not be able to see through the foggy gas today, and astronomy would be a much more difficult occupation to pursue.

Furthermore, current observations show that the vast majority of large galaxies in the universe contain supermassive black holes. That means that most galaxies have the raw ingredients to host an AGN or QSO, and possibly every large galaxy has undergone (or will undergo) AGN or QSO activity at some point in its lifetime. This makes them an extremely important part of the aging process of galaxies, so the more we understand them, the more we understand how the universe ages.