Same reason you don't publicly advertise other information yourself, no matter how easily exposed they are.
Your real life name, for example, is in itself not really a confidential thing. But you dont parade that around the internet.
In my country, you can do a public search for VIN or license plate number, and track it back to the owners name and lien (if they have one)
I think its more along the lines of what
@holmgang is saying. The same reason people dont (tend) to use their real name in an internet forum (although there are plenty of user names here that look like real names). When you buy a home, that is public information, so if someone looks up your address in a local registrar, they can find who owns it, but you typically dont go around posting your home address.
When you take your car into tesla, or call them about it, they will sometimes ask you for the last 6 of your vin. Having the last 6 of a vin, along with someones name etc, could possibly be used in "social engineering". Since there is no gain at ALL from posting your vin (it doesnt help anyone, tesla doesnt assign vins exactly sequentially, etc), there is no point in "over sharing".
TL ; DR version...
No benefit by posting it because the information doesnt help anyone, yet the information can possibly be used as one more piece of information that someone ELSE could use to prove that they are "you".