Uhm, those countries that got "some" amount of migrants which wasn't massive (only Jordan has more than 600k refugees) and certainly they weren't welcomed despite the rhetoric by EU (i mean they are welcome AFTER they survived and weren't drowned?), they NEVER tried to integrate migrants and refugees. At the entry countries most of them simply thrown in concentration camps financed by EU, later on they were getting returned back to Turkey, Libya etc.

Now of course there was a plan about distributing some migrants BUT let me remind you that those quota NEVER achieved, most european countries never received the amount of refugees they were "obligated" to.

The distribution plan wasn't because refugees gathered for example here in Greece and they wanted to stay here, not at all, most of them wanted to leave the country. It was only a passage for them to other countries. Many people had family waiting for them. What happened? Walls were raised. Borders were closed and Greece almost kicked out of schengen (informally it was suspended). Obviously the government was forced to accept the EU plan about keeping the migrants in concentration camps and distribute some people around the europe (that again never really happened other than a small extend). Later on the EU-Turkey deal happened.

Nowdays that xenophobic, anti-immigration feelings are in rise you can hear that plain and simple even by moderate politicians that when syrian war is over refugees are out of here.

In other words, there never was an open borders and integration policy that failed. It is the same fascist policy by EU that getting people killed or rot in prison.