I guess that must be true of the political elite in the major (remaining) EU countries, or it wouldn't be the policy, right?
But for, say, Hungary, where I have a lot of experience, I'm pretty sure basically nobody thinks "increasing integration" should be the goal. Well maybe some tiny minority who happen to work for the EU itself.
The integration everyone cared about already happened, except for the currency integration which will never happen. (IMO good that it won't.) Now you have one side that would like to use the EU as a cudgel for rule-of-law questions but only without interrupting the flow of money; and another, more powerful side that uses the EU as a dog-whistle for nationalists as long as it doesn't interrupt the flow of money.
I can't speak for "Europe" (neither can Brussels) but I know a lot of people in Germany who also think there has been quite enough integration already, thank you. Try ordering an espresso in Berlin without speaking English.
(I neither supported nor opposed Brexit as I'm just a dirty foreigner in the EU either way, but I have sympathy for those who did so on principle.)
