"I think it would be more natural to have the "input" button cycle through the inputs"
By using the up/down arrows, a user is able to access the desired input a little quicker than if it were a one-button toggle.
For example, if you were in Video 1, but wanted to toggle back to DVD, you simply press "input" and then the "up arrow".
With a one button toggle, you'd be forced to go through all of the other inputs before arriving at DVD.
Best,
Scott