1 For a soft, easily accessible target, say the entrance of a hotel, you could already just park, get out, and walk away with say a 1 minute timer to go off before anyone could react if they even noticed.  So no gain in capability there.  For most of the more critical targets, they've already closed roads or put in barriers that you wouldn't get an empty car through.  Plus, of course that most of the bad guys that would be interested in this capability have no problem with having a driver in the car.

2

It would seem I'm not the first person to think of this.

David, I'm thinking of someone more like the Unabomber, who could easily have manually delivered all his bombs personally but certainly would have been spotted doing so. By sending his bombs through the mail, his reign of terror lasted for years.

It's true you can drive a normal car and set it off -- but you'll be seen on a security camera. If you do it my way, though, there may be no way at all to trace you. (For instance, you steal the car, so it doesn't matter if that gets traced.)

3 I did say "most."  For the dedicated and skilled fanatic, there are already many ways to do very bad things.  Fortunately, most of the people who have the skillsets to take advantage of the means already present, don't have the motivation to do so.  To that extent, yes, it desirable to keep the means at least somewhat exotic, not something every Joe on the street with a grievance can get his hands on without a significant amount of planning.
It would seem obvious enough to make sure that self driving cars won't drive without a person in them, and given current technology, it wouldn't be difficult to add "picture, voice recording, and fingerprint of the person who input the destination" as something stored in the black box.  Of course it would be possible to defeat these things, but that again takes it out of the realm of everyday Joe.

4 Unfortunately, IS already has them: The IS research and development team has produced fully working remote controlled cars to act as mobile bombs, while they have fitted the cars with "drivers"; mannequins with self-regulating thermostats to produce the heat signature of humans, allowing the car bombs to evade sophisticated scanning machines that protect military and government buildings in the West.