Yes, I agree with you, but the problem is that at the beguing the UE was just an econimic organization, in 1950, the French Foreign Minister Robert Schuman proposed integrating the coal and steel industries of Western Europe(This part of Europe is very rich in coal&steel, and its control was one of the reasons that made WWI & WWII beguin). A a result, in 1951, the European Coal and Steel Community (ECSC) was set up, with six members: Belgium, West Germany, Luxembourg, France, Italy and the Netherlands. The power to take decisions about the coal and steel industry in these countries was placed in the hands of an independent, supranational body called the "High Authority". Jean Monnet was its first President.
From three communities to the European Union
The ECSC was such a success that, within a few years, these same six countries decided to go further and integrate other sectors of their economies. In 1957 they signed the Treaties of Rome, creating the European Atomic Energy Community (EURATOM) and the European Economic Community (EEC). The member states set about removing trade barriers between them and forming a "common market".
In 1967 the institutions of the three European communities were merged. From this point on, there was a single Commission and a single Council of Ministers as well as the European Parliament.