Re: Private sector needs to show the public sector how it is done
Armstrong took manual control of the last section of the computer landing in the LEM and drifted it along to find a flatter LZ - because it missed the target due to wrong data, and it wasn't possible for a human to see that until it had nearly landed.
With a hand over the "hard abort" button that would put the computer back in control and throw them back to the CM. That's still the closest to actual off-world piloting ever done. Perhaps the same will be done for a manned Mars lander, but I doubt it.
Apollo 13 did one or two 'manual' burns on a "we'll correct it later when the computer is running again" basis.
However, the burn was still pre-calculated by the boffins on Earth, the crew's job was to keep the craft in the same orientation during the burn.
Not to time the burn, not to work out how long to burn for or which direction to do it, and not even to know that it needed doing at all.
Finally, Gemini etc crews didn't do the rendezvous, just the final docking. Computers got them within a few hundred metres and at near-zero relative velocity, humans only handled the final touch-and-grab.
- Compare taking a ship across the Atlantic to New York with going the last 100m to the quayside.
Humans are also rather poor at it, demonstrated by how much practice was needed to get a small number of extremely experienced and highly trained individuals to be able to do it at all. (And how dented a lot of ships are! The big ones auto-dock now.)
Today it's mostly not done - grab the thing with an arm and drag it into place.
The big advantage a human-crewed mission has is being able to repair stuff. If the computer breaks, a human can turn it off, replace bad components and reload the software. A computer can't do that for itself.