In Adventure 02 Episode 44, Ken Ichijouji is kidnapped in a truck that's right-hand drive. His friends are chasing after him in a car that's left-hand drive. Is it true that a LHD vehicle in Japan is considered to be a major status symbol with a high resale value?
Sort of, but not really. For it to be a left-hand drive vehicle, it would almost certainly have to be an imported car, and it is true that "foreign car = you're rich and have status" used to be a stereotype, but nowadays people will get it because they wanted to invest in a specific model of foreign car for some reason (maybe they were dissatisfied with domestic Japanese-produced ones, and the only models they liked were left-hand). A lot of people will also outright avoid it because of how inconvenient it is to drive in Japan's road system, which isn't compatible with it at all, and it's also much more difficult to keep it maintained in those circumstances.
Of course, that doesn't mean having a left-hand drive car doesn't come with some kind of money and status at all, because buying and maintaining an imported car is expensive, but since the Kido family is a prominent and esteemed family of doctors, it's reasonable to think they'd be able to afford it and would be willing to put up with the trouble if they consider the car to be important enough, especially since Shuu seems to be a traveling scholar. It's a family that tends to be picky and low-compromise, so this probably falls in that category.
Incidentally, Kyoko from Cyber Sleuth also has an imported car (well, putting the other considerations about its, uh, nature aside). While it's not mutually exclusive, I think the modern association with it is probably less "rich and elite" and more "hipster and unique".















