Though I do not do it overnight or when I leave my apartment...when I'm around home I will stay logged in just for the background noise of Lavender Beds to echo throughout my home. It's kind of nice, as I am not a city person and grew up in a quiet place in a farm town. Unfortunately for my job, I am forced to be in a city environment for the time being. This is the reason I like to leave my character afk sometimes when I'm doing other things.
That, and if I'm needed by LS / FC friends, they can just /tell me and I'll be right there ready to go for them.