Why do people hide their license plates in the EU?
It's a matter of privacy.
The thing you definitely determine from the license plate in some countries is the county of the registered car. In small countries some counties have a small number of registered vehicles and that eases tracking one.
Other things you may be able to determine in quite a lot of EU countries:
year of birth of the owner (since some use 2 number character in the plate number)
name of the owner (since many use the 2 or specially 3-letter abbreviation of their name)
Example: a car in Romania with the number CT-90-GEO will give you quite good information: the location of the registration is in the Constanta county (abbreviated CT for vehicles) and the owner is named George and was born in 1990.
So many people prefer not to release something like this in the wild.
It is to protect the privacy of the individuals.
Imagine that you can link the license plate of a car to the owner. You take a picture of a car in Berlin and share it in the internet, you will be giving this information to all persons on the internet that the car was sighted in Berlin and thus violating the privacy of the owner that might not wish no one knew he was in Berlin. European laws protect the individual rights.
You can take the pictures but you cannot share them publicly without protecting the faces or information that can break someone else privacy.
In the UK people often obscure licence plates in photographs they post online to protect themselves or the vehicle's registered keeper (often the owner) from "number plate cloning".
Number plate cloning is where someone acquires licence plates by having them produced without providing proper documentation (1). This is usually done in order to steal the registered keeper's identity, making it harder to attribute criminal activity committed in a vehicle to the actual perpetrator (2).
Posting pictures of your licence plate online makes it easier for criminals to find licence plates to clone, especially when attempting to match the make and model of another vehicle they are in possession of (3). Cloning the plate of a vehicle with the same appearance (make, model, colour, body type) means that everything will appear in order if a cursory check of the plate is carried out.