Probably the only things I find annoying:
- can't grab additional quests (It's annoying if you want to grab more quests but... yeah)
- you can't change jobs (It's fine because if you level your shit you can still change your equipment around. You just can't work towards leveling a different class if you aren't on it when you join the multiplayer)
Minor-ish inconvenience:
- you can't advance in the story
- you can't respec your character
It's fine due to the change:
- you can't use quick map teleport [due to a switch in how teleport works in co-op]
Why would you want to:
- you can't change your character's appearance (hair styles)
- you can't interfere with the host's housing decorations
- you can't use the horse (if you're not the host)