With the version - "An example of a joint cognitive system is self-driving cars, where a person turns on and off the driving." why do you think it doesn't work?
Hello again, deepcosmos—I don't think that that sentence doesn't work. That sentence is fine. We weren't talking about that sentence. We were talking about the sentence in which "self-driving cars" comes first.
Instead, should it be grammatically written, "An example of a joint cognitive system is that of self-driving cars, where a person turns on and off the driving"? If so, the existence - that of - is essential in this context?
No, "that of" is not essential. Indeed, in my opinion, it makes the sentence worse, precisely because there is no need for it. Notice that nobody would say something like "An example of an ice-cream flavor is the example of chocolate."