Connotations arbitrary and invisible are connotations that don’t really matter anyway, but let’s get some idea of the issue reading some excerpts from the Wikipedia.
The search for a symbol began in 1950 when a committee was set up in order to look into the question of a European flag. There were numerous proposals but a clear theme for stars and circles emerged.
Richard von Coudenhove-Kalergi proposed that they adopt the flag of his International Paneuropean Union, which was a blue field, with a red cross inside an orange circle at the centre, which he had himself recently adopted for the European Parliamentary Union. [See Letter to the secretary general of the Council of Europe from Richard Coudenhove-Kalergi, Council of Europe.]