Actually, that is exactly what we're talking about. Why would you doubt it? You not only need to keep the helicopter oriented, you need to keep it in the same place, i.e. you need it to follow a zero-velocity trajectory. Why would you think that this is any different from a regular autopilot?
The kind of system I'm talking about here, on the other hand, is essentially a physical model of the three available controls and how they interact to move the aircraft (and thus predict how the aircraft will be moved); combined with actuator-sensors, accelerometers, and gyroscopes to read off how the aircraft is being affected by those controls (and thus correct the prediction)—enabling you to translate linear movement of a flight-stick to linear movement of the helicopter. It's a dynamic torque model feeding a control system, with a user-supplied reference point. You can make an ASIC that does that and put it through fuzz-testing for literally every potential input combination it'll ever receive.
Yes, said ASIC might physically fail (even after you've done an extensive burn-in test)—but, given the tolerances we have in making ruggedized solid-state electronics these days, vs. the tolerances we have in making mechanical systems, it'd be the least likely part in the control chain to fail.
It is true that state-of-the-art navigation systems operate the way you described. But airplanes have been flying for over 100 years, and there have been autopilots for nearly all of them (the earliest autopilot dates back to 1912). The vast majority of airplanes flying today do not have state-of-the-art systems.
Helicopters can also have advanced and full integrated routing systems that will complete an entire trip from A to B, just as fixed-wings can have a simplistic input-to-output linked autopilot that just aims to keep the plane level and with the same heading.
So yes, an advanced system is more complicated than a simple system, but both systems can fail. And since that is inevitable, it's usually better to have a complex system with redundancy that will tolerate failure, than a simple system with no backup that will lead to catastrophe.