In practice that would mean a lot more head/tail accidents, I've seen that happen plenty of times in traffic jams from over-eager drivers, sudden stops (either people trying to go too fast or not paying attention), etc.
Yeah, and there would be no reason to increase acceleration -- increasing the acceleration only aids in this project because it shortens the time when the car behind the stopped car in front of it can get up to speed. If the cars are all talking to each other -- they can all start accelerating at the exact same time and rate as soon as the light turns green etc.
There's also the frequent problem of split attention when you're accelerating like that. Often you may be trying to change lanes, and checking a mirror for an opening. Even without that kind of better communication, computers are just better at tracking multiple data points at once.
That's true only when every car is a self driving car. In the interim, if only a subset of cars is running Level 3 autonomy, then including a quick acceleration into the adaptive cruise control is a good way to minimize these phantom traffic jams.