It just doesn't seem right that you have to log out to see the live site. It's going to be really difficult explaining this to my client. If they want to compare a live page to a draft page, they need to log in, open up their page on the draft site in a new window/tab, then log out of the admin area, open up a new browser window or tab, and open up the page on the live site. Or I could ask them to add "?stage=Stage" or "?stage=Live" onto the end of any URL they go to while logged in, which is going to really confuse them.
Can't you just default the "stage" parameter to "Live" unless it's specifically set to "Stage"? That seems like it would really simplify this draft/live site comparing process.