You have Juncker backwards. He was saying internal EU borders are a bad idea.

Rejecting all borders is a tenable ethical claim - indeed it's hard to justify why states should exist in most ethical frameworks that value human equality - but Juncker didn't go there.

But yes, Britain sabotaged the EU, including its having a joined-up defense and border strategy. Indeed, you might expect the departure of the most Eurosceptic nation to strengthen the EU.