Re: "But the train did come to a complete stop just 7.5cm from its intended stopping point"
You are not aware of the fact that on the London Underground's Central Line drivers are not even allowed to voluntarily run under manual operation ("Coded Manual"), unless it's a Sunday and they are outside the central zone?
It's simply a result of human drivers not being able to safely run the trains at the short spaces and stopping distances required in central London. I remember a couple of years back when there was a computer failure on the Central Line and every train had to fall back on manual operation. Instead of a train every 90 seconds it became a train every five minutes (wholly inappropriate for central London, causing dangerous levels of overcrowding) if you were lucky. A train every ten minutes was more common.
There are a couple of problems with human drivers. For one, they can only see the train ahead of them, if they are lucky. A computer can see all the fifteen trains ahead of them and pre-empt a "bunch-up" because six trains ahead there is a slower train. It also turns out to be quite difficult to train drivers on stopping on time. On the Central Line a train is expected to come into the platform at full speed and only initiate braking roughly halfway along the platform. Human drivers tend to find that unintuitive and feel they need to brake when the station is approaching. That makes running railways with over approx. 25 trains per hour (tph) practically impossible. Some metro systems run up to 36 tph, thanks to computer operated trains. Finally, computers are never hungover, had a poor night's sleep or in the middle of a messy divorce. That doesn't mean the Central Line doesn't have people referred to as "drivers" in the front of the train. They are vital in deciding when to close the doors and when to tell the computer it's time to depart, and vital in evacuating the train in emergencies. It's only the train movement that's handed over to computers.
On main line railways there are other things to bear in mind than in metro systems. Level crossings for instance. It would come as no surprise that all main line railways experimenting with ATO (such as the Shinkansen or the Dutch dedicated freight route "Betuweroute") are fully grade separated.
That said, even main line trains have been relying on machines for decades. A stopping distance of 1500 metres is not unusual for some trains, far beyond the visual range of a human driver, so they rely on signals to warn of problems far ahead. It's also why train drivers are "route-trained", they are typically not certified to drive trains on routes they haven't been trained on. Because they need to know minutes in advance that a sharp bend is coming, or to expect a signal two kilometres ahead.
In short, it will be quite some time before many main line trains will be running without people in the front, but it has also been quite some time since trains were run without relying on computers to make everything work safely.