What are the main challenges that the EU has posed to the European nation states?

The functioning of the European Union is founded on two foundations: The Treaties, and the enforcement of the Treaties. The Treaty on the Function of the European Union, TFEU, defines how Member States should interact with the Union. It binds the Member States to obey it and the subsequent treaties, as they are signatories.
The EU aims to integrate the Member States as part of a Single Market, causing the TFEU to overlapse on sovereign powers, such as regulating taxes, border control and judicial process. Article 30 of the TFEU orders the removal of all trade barriers within Member States ‘Custom duties on imports and exports and charges […] shall be prohibited between Member States’.[1], which hinders taxation. An unprecedented case saw the use of Article 30, in 1963 during the Van Gend en Loos v Netherlands Inland Revenue Administration case.
The Dutch Tax Authorities had to remove barriers under the ruling of the European Court of Justice.[2] The European integration has led to a complex re-organization and redefinition of every state’s core structures, and ultimately lead to the loss of their own monopoly on policy and decision making.  The ECJ has dealt with several cases on taxation, free movement of goods and protectionist measures imposed by Member States. The Doctrine was developed by the ECJ in its conception of a ‘new legal order, of international law for the benefit of which the states have limited their sovereign rights’[3]. The EU, in creating a uniform common market between different states, decided that EU law would talk precedence over national law. One case was R (Factortame Ltd) v Secretary of State for Transport, where the ECJ overruled and declared the constitutionally voted by UK Parliament Merchant Shipping Act 1988, null and void. The ECJ, in enforcing its Treaties, has found that the Act of 1988 went against EU law and enforced the Treaties through the Doctrine.
However, the Supremacy of EU Law over national law has created a new challenge; a sense of deficit of Democratic process and institutions within the member states and a divided support for the Union.
 The EU has been characterized by its nature as something sui generis, unique. The structural deficit in the EU can be seen by the lack of democratic legitimacy, where it has historically relied on the ‘common belief that government is responsible to a given people, accountable to that people, and obliged to serve the interests of that people’.[4] However, the inter-dependency between Member States and communities have reached a point where democracy has lost its traditional values – as something within a specific sovereignty, defined by clear sovereign interests and self-governed by the people it represents - to something foreign to the citizens. Furthermore, the seemingly growing interventions of the European Union in intra-national matters seem to have contributed to a rise of antiestablishment, populist and nationalist political parties within member states. These parties, often referred to ‘eurosceptics’, are the reaction to an increasing worry that too much sovereign power had been given to Brussels; when the EU centralizes power in a federal manner, rather than disperse it between its constituents.[5] These political movements gained more popularity since the Eurozone Crisis, as for many EU Citizens, the way the EU handled the Crisis clearly lacked democratic representation.
[1] TFEU, Article 30[2] Craig; de Búrca (2003). p. 182.[3] Case 26/62, Summary - 3[4] Pauly and Grande, (2005) p.11[5] Kim and Jung, (2019) p.56