That does seem like the biggest problem with this idea. The entire surface doesn't have to be writeable, though. You could cover part of (most of?) the desk with a second surface, fixed around the front and back, that would remain stationary as the paper moves.
A nice compromise would be to use butcher-paper that's less wide than your desk is deep, leaving perhaps the back third of the desk uncovered. That way, you can put your various permanent pieces of desk furniture --- pen-pots, charger cables, paper trays, whatever else --- at the back of your desk and still have the front two-thirds as a rolling writing surface.
That also probably makes it easier to use 100% of the depth of the writing surface, because reaching right to the back of the desk isn't really practical. A relatively standard UK desk is about 800mm, or ~32", deep, so having the back 300mm/~11" uncovered would work out pretty well.
Edit: Just realised that this comment describes a solution that's functionally equivalent to panic's comment one level above[0], though does vary a little in the method of implementation.
I'd love to have a setup like this. I would probably let small objects pile up on its surface though, which would make it hard to turn.