The EU can mostly integrate migrants from within the EU, conflicts because of East to West migration aside (see Brexit). It can also integrate migrants from other countries with shared cultural values like the US, Australia, Japan, etc. Basically other democracies and allies.

It has consistently failed to integrate other migrants, especially from the MENA countries. At this point, experience has proven that such large integrations are and will be out of reach for the EU.

The only logical conclusion is therefore that the EU has to prepare to reject further migration. Even hopeless cases like Sweden are starting to take action in that direction.