Why draw the order instead of writing one?
Because every slot is worth something and everybody knows it. First gets an audience that is awake, last gets one that is checking the clock, and the middle gets the fewest questions. An order somebody wrote is an order somebody can be blamed for.
Drawing it in the room ends that before it starts. The session log keeps the sequence with the time each name came up, so the order is still there when somebody asks whether they really were fourth.
Does it work for teams rather than people?
Yes — one entry per team, spun the same way. A team name is a shorter label than six people’s names and reads better on a projector, which matters when the wheel is the thing everybody is looking at.
If teams differ in size and the bigger ones should present earlier, weight them. The segment widths change with the weights, so nobody has to be told that the odds were adjusted.
What if somebody arrives late, or drops out?
Add or remove the name and carry on. The wheel redraws immediately and the draws you already made stay in the session log — you are changing what is left to draw, not rewriting what happened.
To start over cleanly, reset the session. That puts every name back on the wheel and clears the log, which is the honest way to redo a draw somebody objected to: visibly, rather than by spinning again and using the second answer.
What else is this wheel good for?
It is the name wheel in elimination mode. Where the agenda has numbered slots rather than names, the number wheel draws the slot and you fill it in.
Split the same list into sides rather than into an order and it is a team draw. The same wheel with a December list on it is a Secret Santa order.