Two of the problems I most immediately recognize in the animation interface are:
1. The fact that you can only move one degree at a time, e.g. rotate X, translate Y, etc.
2. The general awkwardness of using a mouse (or two), particularly the fact that you have to click on everything before you want to control it.
What if instead of a mouse, we hooked up each computer to a mixing board with 6 or (depending on if squash and stretch is being used) 9 sliders? Three would be devoted to Translate XYZ, three to rotate, etc.
Instead of clicking a joint (assuming we end up using joints, of course) and then clicking and dragging the translate/rotate/scale tool for each channel, all you'd have to do is click the joint (if that) and slide the sliders back and forth, even simultaneously, in order to get the position you want. Since the sliders have limits and Maya doesn't, the knobs can be used to adjust the "strength" of the slider. Or if the slider has already reached the end, the on/off buttons for each track (not in drawing) can serve as toggles for which direction on the slider is a positive or negative transformation. I feel like this can make things substantially easier because:
1. We're more used to moving our fingers independently of each other than our hands (piano, typing, ...mixing boards, etc.), so learning to move multiple channels and degrees at the same time would ostensibly be more intuitive than learning to use a mouse with your left hand.
2. The sliders are just as one-dimensional as the channels, and can move more smoothly than a mouse for this reason.
3. There's no switching between tools or clicking on the right arrow/circle/cube in order to select/move it.
Although using this in the "one shot, multiple simultaneous animators working in real time" method would prove very time efficient, I feel like it would even cut a lot of time out if it was used by individual animators doing keyframe animation.