I was thinking that we first need to have this in Houdini and then we could apply the tech developed for that in Maya.
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WIP: Bezier Deform Offsets per control.
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This is Houdini and it is basically what I would expect as a solution for my RFE. Though I would also hope for additional sliders for arbitrary attributes that could be generated when needed.
I think something similar can be then achieved in Maya with (callback) scripts and custom attributes. You would then maybe have a shelf tool to create a special NURBS curve that has some scripts associated with it.
I have have seen in the Maya script editor, that even though the vertices do not have scale and rotation values, the calls are executed when you use the gizmos. (But I don't know whether you can get those calls.) The additional information could then be stored in custom attributes.
Obviously there would be a bit of overhead, but I think the overall workflow possibilities would make it worth it.
Maybe it makes sense to use custom NURBS shapes for controlling the knots of the curve (instead of locators, because those don't properly show scale).
In my experience it is desirable to have input curves as independent objects. The other important thing is that they are easy to use.
To clarify why it's useful to have input curves as separate objects: They could be (re-)used by multiple different scripts, models and HDAs. They can also be moved across scenes. They would not loose information from updates etc.