Standby instrumentation has operated off a stby pitot and static port for decades, problem is that they are generally the same as the others, just an additional system that is stand alone and pneumatic/mechanical, old ones not requiring any electricty to operate.
I feel the cost of an aditional system would outweigh the benefit. Feel confident that mfgs's, aviation authorities and airlines feel the same.
Another problem is, if you have a pitot probe that pops out in clean air in an emergency you also need a static port and alot of effort goes into making sure the static source is clean (mostly flush skin within proximity to the port).$$$$$$$$$$$