Toyota has enough UX data that they added "brake assist", turns out that a lot of accidents happen when the user stomps the brake, but then releases, just never presses it hard enough to come to a complete stop, or was trained before anti lock brakes.
https://www.youtube.com/watch?v=grcuorbrYxA
Another scary thing about braking is that most cars probably don't have their brake fluid changed often enough; most owners and even dealers treat it as a lifetime interval, when it may be closer to an annual thing interval.
Driverless cars simply don't have the mileage yet to prove they are safer than driverful cars. But there's also no indication they are less safe, based on casualty rate so far.
There is an indication that they're less safe! They have (very conservatively) 5x the number fatalities per mile driven! Now, look, the error bars on that estimate are of course massive. It is plausible that they are much safer and they just rolled the dice and got unlucky. But this is data, as long as you include the error bars.
Something that is endemic in HN discussions of driverless cars is commenters who dramatically overestimate the dangers of humans driving. Like an order of magnitude or more. You see it all over this thread, in which people imagine that killing one pedestrian in like let's say 10 to 20 million miles driven (with those miles overwhelmingly done in unchallenging conditions) constitutes "vastly safer than human drivers" rather than "vastly less safe than human drivers."