What is the benefit to owning legendaries?

I’m a huge fan of Pokemon, but I’d definitely consider myself a very casual player. I haven’t played Gold/Silver, Ruby/Sapphire, or X/Y. But in the games that I have played, there doesn’t seem to be much use for legendary outside of dex entries. With the exception of the DLC games, I feel like there’s not much game left after getting the box art legends to actually enjoy having a legendary. Maybe I’m just not experienced enough to know. But where is the post-story utility in having legendaries?