A couple of reasons come to mind, basically the ones you mentioned, plus a wide variety of electrodes for different purposes, including many specialty ones you can get in small quantities. Most specialty MIG wires are only in large spools, and sometimes require different gas. So for a small hardfacing job, or heavy stainless weld, it might be more cost effective to go stick. Maybe it's just me but it seems like stick welding can be more ductile in an as welded condition. Another feature is the ability to run longer leads, great if you are up on a ladder, or crawling through tight areas where you can't drag the MIG machine close enough. Jodi showed a great example where getting a weld between things was too tight for a MIG gun, but you could poke a stick through the gap and get the job done. It's just another tool in your belt, and once you have learned that, you might find other uses.
Long arc, short arc, heliarc and in-the-dark!