How to DROP an object when releasing Child Of constraint? I noticed due to the parenting system of Blender Child Of constraint does not modify the object's location/rotation in such a way we can copy or interact with it.

So when you drop influence of Child Of constraint, the object snaps back to it's original location as seen before instead of simply being suspended in the location it was guided to by the constraint.

The problem is this: How do I get an object to release it's child into mid-air, so to speak, so that physics can take over cause the object to drop?
I assume you are creating an animation ? In that case, a trick you can use is just to set the position of your object at the exact position it was before, on the frame you drop the influence option to zero. Then, if you run a physics simulation, I think it should work.

Let me know if you have any question !