That’s not something a single control point can do on a NURBS curve or surface.
Try selecting multiple control points that are in a row.
Rotate the row of points and the curve or untrimmed surface edge will change.
About all you can do to change the shape of a curve or surface with a single control point, is to move it closer or farther away, or change the “weight” of the control point.
This is a degree=3 curve:
Yes, I know how the curves behave currently, I know in NURBS you have to select multiple control points to make what I wish.
That’s why it’s a wish.
What if in case of a polyspline, joint nurbs surfaces sharing an edge. If rotating a control point could change these surfaces by at the same time not breaking their common edge that would be valuable.
What if by rotating of the pole point of a sphere you get this:
Maintaining proportionate rotation and distance between the U and V rows.
A single rotation of a control point.
Sounds like what Mirrakoi’s Xirus plugin does: