I understand that this would be complicated to detect if you had a script running all the time, and would cause performance issues. So what about a script that only runs when you activate a bed? Have it check to see if you have a follower (easy) then find a nearby unowned bed with, say 20 feet (easy?) and then sleep them in it (???).
When I wake up, I would so much prefer to find my follower still sleeping on a bed nearby and have to wake them up, then for them to be up and raring to go already. This problem is even compounded in my home, where there's a spare bedroom that nobody uses. Why is that bed there? And why, if nobody that lives in my house is going to sleep in it, can't I?
This happens a lot in dungeons too. I clear out a certain section, then bed down in a roll for a while. There are usually 2 or 3 bedrolls in a spot, sometimes I've seen quite a few of them. Follower never does sleep in any of them. It's not game breaking, but it's a little creepy. It would just make for a nice touch.