I had not seen that video before, as you say works some of the time.
I would say that video shows you the exceptions to the rule, using a circle is misleading.
I have tried the workflow for redefining the plane, and at times the sketch can be reveresed, front is now behind, or went 90 deg, or at least orientated in a way I didn't want, so I try to avoid it.
What you did is absolutely normal, and in your second video, it demonstrates the bottom of the extude lifted to the top step.
Normal, you are not asking to move the sketch, just it's alignment, and because the sketch is populated with geometry, that geometry goes for a ride.
Half of Bens workaround is about what you can get to work when not parallel to the original, the point you make,
but the first half with the "symetrical" sketch attached to World Origin, I reckon would be the only time it is reliable.
Would you make a workplane on a face, that is not my normal workflow either, can do it and there would be good reasons to do so,
but with sometimes unexpected results as you see. (green line example)
Can I manualy set the centre of sketch on plane? No.
A Workplane has no dimensions, or geometry, so how can you find the centre of nothing?
except that, only after you select it, or "create sketch" on it, Fusion will project the World Origin to it, so you can snap the sketch to it.(World Origin's reference point)
Always many ways to do the same thing.... Have you seen the video 9 ways to make a cube?