Simplest case, two adjacent groups will share CPs on their common side. Lots of separate groups will have CPs in common.
I think Group locking and hiding would be one more thing for people to lose track of and not know what's going wrong.
Interesting idea, I don't know it the math of splines allows it or not. Basically the bias handles are normally parallel to a line drawn thru the two neighboring CPs. When you "adjust bias" you are making an offset from that original default, not an absolute direction like you do in a vector program such as Illustrator.
A new data element would have to be added to every CP to somehow make the bias handle ignore its natural inclinations and instead stay oriented to... the model bone? Another bone? World space? Something else?