There's just this wrangle over how to manage that best... What do we need, and how much of it?
It's interesting in this regard to have a look about how Europe was managed over time since the EU history isn't as linear as some might think.
1951-1973: opening markets and reconciliation
In the post-war era, European countries pushed for a reconstruction of their economy based in opening successively some specific markets: coal, steel, atomic energy, agriculture.
This was fully lead by national heads of governments and ministers such as Adenauer, de Gasperi, Monnet and Schumann, with the double objective to promote reconciliation in tightening our bonds and to redevellop countries which were then very late compared especially to the United States. We were for sure in a very different period of History compared to nowadays.
1973-2001: economical integration
After the large success of the markets opening, French and German leaders especially pushed for a very ambitious plan of economical integration. It started with the UK entry in the EEC, but it moved much further than that: creation of the European Parliament, strengthening of the European commission able to propose plans to be submitted to national leaders, creation of the single market, the Schenghen area and the single currency.
This period was both the pinnacle of Europhilia and the beginning of its end. This was indeed the golden age of Eurocrats, the President of the Commission being nominated and having massive power to determine the European strategy (but still with the required consent of country leaders). And meanwhile, it's also the period of a massive economical slowdown which has lead to the first European crisis. Indeed, establishing the single currency has lead to the first tensions between countries, especially regarding monetary policy.
2001-nowadays: the return of nation states
The lesson taught by the difficulties to implement the single currency, and more precisely the Maastricht criteria, has lead Schröder and Chirac to reduce the influence of the European commission in order to better control it. The enlargement to the east was used as an opportunity to massively reshape European institutions, and especially the commission, which became more centered in defending national interests (one commissioner per country) than the common European interests.
The failure of the European Constitution has also marked the end of the European dynamic. And once Schröder decided with the opportunistic consent of Chirac to disrespect Maastricht criteria, it made it clear that national leaders were taking back control over past European commitments.
This evolution never ended to grow. After the success of Agenda 2010 in Germany, Angela Merkel was leading a country completely dominating Europe economically speaking. This, together with the strengthening of national leaders over European institutions, has totally destabilized the balance of power in Europe.
The debt crisis, and later on the refugees crisis, have proven a total lack of goodwill among European leaders to try pushing forward a quick solution to curb those issues at a European scale. Merkel signing a deal with Erdogan on refugees, without even giving notice to its European partners about it, has marked the pinnacle of this evolution.
The Brexit is clearly the direct result of this evolution. Europe has proven itself unable to master crisis, and the power of Merkel on determining the European agenda according to the only German interests has seriously questionned the purpose of Europe as an institution. Yet, we all see clearly that not only a full dissolution of the EU would be extremely difficult to implement, but it wouldn't even solve the incapacity of our countries to solve shared crisis.
And tomorrow ?
I have seriously no clue where Europe is heading to, and considering Merkel is heavy favourite to win again the German federal elections in october 2017, there is a strong chance there won't be any significant change before several years.
Nevertheless, a majority of both pro-Europeans and Eurosceptics agree that Europe is currently dysfunctional. How this will be managed? Only time will tell.