3 Things:
1. "Driver-less cars have vastly shorter stopping distances at all speeds"
I can understand your expectation of reduced stopping distances due to the near-0 reaction time made possible by sufficient computing power. However, I wouldn't describe the computer's advantage as anything close to a "vast" one. There is no mechanical advantage to braking that is inherent for a driverless car and the difference in stopping distance due to reaction time is less than 1 car length (~10ft) at 30mph assuming the human driver has an average reaction times (0.25s). The advantage is still limited to roughly ~25ft at 60mph. That advantage is simultaneously significant and insignificant in that incredibly common outside factors will more than account for that disparity if not controlled for in the AI's programming. Tire pressure, tread depth, brake pad thickness, rotor wear, alignment, etc are all capable of individually accounting for a ~25ft reduction in stopping distance which leads me to my second point.
2. "Driver-less cars should never drive at a speed where they can't stop in time."
Real world driving conditions present so many uncontrolled variables that a speed considered "safe" by that logic will be pathetically slow. The current state of the art in driverless cars is Google's purely autonomous design which is limited to the pace of a golf cart (25mph). The number of variables introduced by vehicle condition and maintenance alone are so great that any vehicle capable of accurately accounting for each one would be impossibly expensive to buy and crushingly expensive to maintain. While all of our cars are capable of measuring speed (the legal maximum is +/- 5mph @ 50mph in the US, but +/-1-2% is most common) and most cars can measure tire pressure (+/-15% for the most common systems which measure indirectly with the ABS sensor), they don't measure either of those things accurately according to manufacturer specs and things only get worse over time. Personally, I can't see driverless cars ever growing past that hurdle, winding up limited to inner-city commuting/taxi duty.
3. "Same is true of balls and other small fast moving objects, they are not going to ping as kids."
This is actually one of the best examples of why speeds will have to remain slow enough to guarantee a negligible stopping distance.
If a human sees a ball roll into the street from behind an obstruction, they will reasonably deduce that there is a likelihood that a kid is chasing after it and slow down before the danger presents itself. An AI will see the balloon or ball and it will have to treat it as either a complete non-issue or as a mortal danger. If it treats it as a non-issue, it will have to be in a constant state of readiness to stop in the smallest reasonable distance, that means limiting speeds to a relatively glacial pace. If it treats it as a mortal danger, it will constantly produce false positives which leads to frustrated passengers when it brakes hard for every trashbag that blows across a 70mph highway.
That's one of my main criticisms of driverless cars in their current state. They are measurably superior in the areas in which human drivers are most flawed, yet their logic leads them to make decisions that no human would ever consider as logical. Even the most state of the art AI isn't even close to being able to account for the nearly infinite number of exceptions that stem from the chaos of the real world and which require an action contradictory to a principle of placing safety first. Just look at the first "unforced error" reported by the Google program where the AI's logic misjudged the actions of a bus due to logic which defined exceptions around the distance needed to merge on to a road. It just went for the merge, turning straight into the side (pretty much in the middle) of a bus moving at 15mph. No human would have made that decision.