So, what if I switched for a day and it ended up being the worst day ever in their existence? What if I picked them, we switched, and everything went wrong?
And this question doesn't imply time-travel, but let's just stretch the possibilities. Would I want to go back in time and be a younger me for a day? And what day would I pick? Sometimes, I think I would if given the chance. There are a couple of days in particular I wish I could go back and change. Of course, there's a part of me that believes the universe would rebound or self-correct and I'd be in the exact same position as I am now. Changing an event doesn't change the people involved. Maybe that particular experience would have been averted, but what's to say the end result wouldn't eventually be the same?
So maybe the answer isn't to go back in time to try to change anything. Maybe the answer is, if the possibility ever presents itself, that I'd go back in time and relieve a day when my life seemed perfect.
And if time-travel is out of the question, which let's say for the sake of cataclysmic paradoxes that it is out of the question, then I'd have to say that no, I really don't think I'd want to switch places with anyone for a day. Life may not be perfect, but it's my life and I've got a lot of really wonderful, if not downright amazing, things going for me.