vertical (straight back and straight through) or angled (arc) plane for putting?
"So if you are going straight back, you are coming off plane and are above it. If it works for you, great, but you are off plane".
The idea of the putter swinging on an arc or angle plane only for it to be on plane is not true.
When dealing with the sweet spot plane you can use a plane that is vertical (straight back and straight through) or you can use a more angled plane (arc). One of the problems for the vertical plane is the USGA legal lie of the putter. If it was allowed to have the lie angle set to where it is vertical or straight up and down the vertical plane would be easier to do.
You can still swing the putter on a vertical plane but you would want to set the putter lie as upright as legally possible. The length of the putter is important and you also have to change the left hand grip were the butt of grip is in the cup of the left hand. This will allow for a vertical plane with the pendulum motion coming from the left wrist joint. This is what a lot of old timers used for putting like Bobby Jones. With the vertical pendulum motion from the left wrist you would control the movement of the pendulum from the right elbow bending and straighten with the left wrist as the hinge.
You could also use the right wrist moving back and forth for this motion but it is harder to control the speed. I also find that if you set the right forearm on the vertical plane and it stays on this vertical plane during the stroke your sweet spot will move back and forth on a vertical plane a lot easier.
In saying all of this is it worth trying a vertical plane or is it better to use the angle plane or plane set from the putter lie angle?
I have found that if you use a shoulder putting stroke that the angle plane is what you would want to use. If you use a vertical plane putting stroke use the left wrist joint as the pendulum pivot point and control this with the right elbow bending and unbending action. There will also be a little shoulder motion with the vertical plane but it is a movement due to the right elbow action.
Both ways must be an on plane movement it just depends on what plane you want to use for putting. Is one better than the other? The golfer will have to find out which is better. I use the vertical plane for putting and a swing trainer that trains and ingrains this vertical plane style of putting.