The same nerve conduction latency exists for your arms. The computer will beat you every time.

Perhaps a humorous example of this: a robot that always wins at rock paper scissors: https://www.youtube.com/watch?v=3nxjjztQKtY

There's a fun parlor trick which takes advantage of human reaction time too: place a hundred dollar bill on the table, let the other party place their hand a few inches away, start your hand a foot above theirs; the first person to place their hand on the money wins, and the other party can start moving as soon as you start moving. Turns out you can easily go around their hand and grab the bill before they're able to react.

It's a shorter distance.

The distance is beside the point. The amount of time it takes for your brain to parse visual stimuli, then propagate a signal to your arms, and finally for the muscles in your arm to contract will be much slower than a computer parsing a sequence of images and then actuating the steering column. The computer is faster both at understanding it needs to respond and at signaling driving systems to respond.