Every state in the USA is different, but in Virginia license plates are easily linked to a name and an address.
It is probably a similar situation around the world too. If you received your plates from a government agency, a private investigator can look up your information. Posting a picture or video that includes your license plate therefore is basically the same as posting one with your full name and home address.
The investigator may have a good reason, or they may not.
The PI may have a legitimate reason for running your plate, or they may not. Either way though, don't make their job easier by having your plates displayed on social media. Depending on where you are in the world too, the investigator may be giving your information to a criminal, or a criminal may be paying off a government employee for the information instead.
Sometimes a license plate is the only good lead an investigator or police officer has.
You were probably thinking, "they can easily just look me up by my name anyway." I've seen countless examples of people who worked very hard to stay anonymous online, but then they posted a license plate image or video.
Investigators can also use license plates to gather information on your friends and family. You post a video that includes your driver driving your daughter to soccer practice. Now investigators know who your driver is. An investigator sees you leaving work with another woman and in her car, not yours. Now they know who that woman is.
License plates provide a lot of valuable information. It's one reason I recommend a street facing residential camera too. Burglars often case the neighborhoods using vehicles, and they will use vehicles to haul off their loot. You'll want those license plate images!
This doesn't only work for cars. It works for other vehicles as well such as planes and boats.
A professional driver who was also a Close Protection Officer got a lot of grief for posting a photo of him dropping off his principle at the airport. There was one problem though that he did not at first notice. He had included the tail license of the plane in the photo.
The driver had given away the schedule, location, and flight path of the customer!
Boats and planes can be tracked in real time using free online sources. Therefore, keep the details of your travel out of social media. No one needs to know your exact schedule or what exact boat or plane you happen to be on. Why give an enemy such valuable intelligence?