Consider human rights. The ECJ loves to overrule government decisions on migration/asylum on the grounds of human rights, they do it all the time. The inability to deport Islamic "hate preachers" was one of the contributing factors in the Brexit campaign, in fact. Yet the moment Austria placed a large fraction of its own population under indefinite house arrest without trial, in violation of the Nurenberg Code no less, the EU was mysteriously silent.
Or how about the rule of law. When eastern European countries were electing conservative politicians the EU couldn't shut up about how the "rule of law" was being violated, though they never quite explained how. Then Latvia's parliament banned unvaccinated MPs from voting, violating the most basic rule a democracy has and at a stroke disenfranchising whole chunks of their population. Once again, the EU couldn't find anything to say about this.
I rest this case with a few quotes from Jean-Claude Juncker, former head of the EU Commission. He said these things whilst running the EU's most powerful body:
"We decide on something, leave it lying around, and wait and see what happens. If no one kicks up a fuss, because most people don't understand what has been decided, we continue step by step until there is no turning back."
"When the going gets tough, you have to lie."
"I'm ready to be insulted as being insufficiently democratic, but I want to be serious ... I am for secret, dark debates"
"I believe neither the French nor the Dutch really rejected the constitutional treaty." (they did, of course)
In the end the, the EU does have values but those values are not the sort of values they're willing to publicly advertise.
Keeping an airtight border is a very expensive task. You can probably be harder to get into than the next country, but in the context of the EU, that's not really a solution, it's just a way to make the problem worse.
Both Hungary and Poland have shown that a modern state can largely prevent illegal crossing of its borders. We have the technology. It's not that difficult. Even easier when you have a sea acting as a barrier.
When the migration happens on a massive scale regardless, it's usually with tacit or explicit establishment's approval.