For me it's just an enjoyment of the broody hen process... and you can't beat watching a broody with her newborns, I could spend hours sitting in the coop just watching chick TV! LOL
Hatching also gives folks the ability to mix breeds easier. Many suppliers don't sell less then 6 or 12 chicks, and sometimes it isn't safe or practical to ship less than a dozen at a time (for warmth and to keep them from rolling around in the shipping boxes in particular) so being able to hatch allows more variety and flexibility in numbers and breeds.
and I think we get a sense of satisfaction out of being in some way responsible for the end results, even if we don't have a major role in the hatching (trust me, the broody gets all the credit at our place, but we are still pretty proud of those little ones! )
Did you "force" broody, or did you get lucky?
If I had a broody, then by all means...I'd let her keep things and it would be AWESOME. Unfortunately, my girls don't seem very interested.