In principle, it does of course make sense.
However, at least here in Germany the authorities would only react if a
German publisher would misuse the logo, and even then they would hard-
ly do more than send the publisher a letter to ask him to stop it. He could
safely ignore the letter for a year or two.
And the idea to complain as a German citizen to, for example, the Italian
authorities about something an Italian publisher has done ...
Unless you put a lawyer behind it, complaints of that kind usually do not
go very far.