From what I've gathered, Kirk got suspended as a cadet, in his third year. He wasn't even allowed to board the enterprise with the others when it left.
That either means he had no commission at the time he boarded the Enterprise, it was a writers error, or he actually was listed as a lieutenant even though he was a cadet under academic suspension..
With cars an everything, it will depends on interpretation, and whoever is writing the story.
It's always going to go back and forth.
Up until Nemesis, we don't see any wheeled vehicles, as if to give the message that they were obsolete. Everything was now anti gravity or hovercraft.
Harry Kim, from Picard's time, doesn't recognize a truck, although Picard in Nemesis suddenly breaks out the jeep.
Before that, even in environments similar to the one where Picard used the jeep, they never used wheeled vehicles.
IMO, it was just a fun piece to add in the story, although it seemed awkward and out of place to some of us.
It's not that Kirk doesn't know what a car is, but that automobiles and wheeled vehicles were (considered) obsolete by his time.
In TVH, Kirk himself walked right in front of a fast oncoming cab, as if he didn't understand the concept of oncoming cars and traffic