[shapefrog]

> require open borders, which the EU insists on

The EU does not insist upon "open borders".

The single market (EU) seeks to guarantee the free movement of goods, capital, services, and people, known collectively as the "four freedoms".

Article 45 covers the relevant things that the EU "insists" on including the restrictions the EU "insists" on - https://ec.europa.eu/social/main.jsp?catId=457

Perhaps you mean the external border of the EU - Article 3 covers that one, and the EU does have requirements that it insists on for this border. It obliges Member States to carry out systematic checks against relevant databases on all persons, including those with the right to free movement under EU law when they cross the external borders. i.e. they actually insist that it is a closed border.