For comparison, a typical ball screw, has positioning accuracy/resolution of around .02mm
It would be useful if CNC machines did a depth scan of the bed before starting to cut, to make sure that the machining plan didn't run the tool into a clamp or something. Not super high precision, just enough to check clearances.
Most of the headaches of CNC machining involve getting the workplace, tools, and clamps in the right place. Only then can the machine do its thing by itself. Help in that area would make CNC cutters more accessible to amateurs.
Some CNC machines intended for unattended operation have microphones or MEMS accelerometers listening to the cutting, to detect when something has gone wrong, like a worn-out tool. Monitoring spindle torque is common. Too little means the tool broke. Too much means the tool wore out.