Why would high-voltage cables have semiconductive layers in their design?
The material described in the patent referred to is not semiconductor material in the sense that we understand it in the electronics field: The material is described as a polymer base "mixed with a conductivity imparting agent such as carbon black".

In other words, it forms a weakly conducting, yet not perfectly insulating, shield layer around the conductor element. Modern parlance would refer to this as a partially conductive material, I suggest.

The application seems to be similar to the use of a very high value resistor between an earthing strap, and the building earth such straps are often connected to.

Referring to the default source, WikiPedia:


  At the inner (2) and outer (4) sides of this insulation, semi-conducting layers are fused to the insulation.[4] The function of these layers is to prevent air-filled cavities between the metal conductors and the dielectric so that little electric discharges can arise and endanger the insulation material.  


On the same page, more information is forthcoming from the section on cable joints, though applicable to the cable itself, as well:


  The black parts in this picture are semi-conducting rubber parts. The outer one is at earth potential and spreads the electric field in a similar way as in a cable terminal. The inner one is at high-voltage and shields the connector of the conductors from the electric field.


While this is not definitive first-hand knowledge, such use of semiconducting, or to be more precise, partially conductive i.e. high resistance shield layers seems to be common knowledge in the literature.