The EU is not unique in this respect, many countries do not give their national symbols legal status: for example the flag of the United Kingdom was never formally adopted as a national flag, let alone enshrined in the constitution, and only has its position de facto. Another example is the absence of a national motto for the United States (before 1956), despite E pluribus unum being commonly used as such.
This system has been criticised for under-cutting farmers in the developing world. The overproduction has also been criticised on environmental grounds in that it encourages environmentally unfriendly intensive farming methods. Supporters of CAP say that the economic support which it gives to farmers provides them with a reasonable standard of living, in what would otherwise be an economically unviable way of life.
The EU has developed from an international trade organisation aimed at improving the economy and thereby fostering peace in Western Europe. Nowadays the EU also bears some hall marks of a more state-like entity, like an anthem, a flag, a common currency, but also representation among other countries in international organisations like the G8. However, other properties of countries, like a fully-fledged defence force, are not part of the EU's mandate.
Some editors believe that the EU will evolve into a true federation in time to come, and the article should reflect this by adopting a structure very close to the style of Wikipedia country articles. Other editors doubt this, or even think it very unlikely, and argue most, if not all, country specific sections should be omitted. All agree that the direction of the EU is hard to predict, and that we should be very careful when writing about this, as it is basically speculation.
There is, however, another issue here: a lot of the culture of Europe (literature, painting, music; or even Roman/Greek antiquity) originated long before the EU was founded. While this culture is undeniably part of the cultural heritage of the EU countries, it is just as much part of the culture of non-EU European countries: Switzerland, Norway, Iceland, the mini-states (Andorra, Liechtenstein, San Marino, Monaco and Vatican City), the republics of former Yugoslavia (Serbia, Bosnia and Herzegovina, Croatia, Macedonia, and Montenegro), and the eastern European Moldova, Ukraine, Belarus, and Russia.
The EU is an association of sovereign states that have agreed to work together in some matters and only those matters. So in those matters (only), decisions are made either by unanimity (in some cases) or by qualified majority voting in most other cases. Neither the Commission nor the Parliament has any authority ["competence" in Eurospeak] to act in any matter that is outwith the scope of the treaties. The EU has many characteristics of a confederation in matters where (by treaty) collective action is agreed but not otherwise.