This is conflating so many things it’s almost impossible to reply.
The EU as we know it is the EU with the Schengen area
EU and Schengen are different things.
There are Schengen countries that are not in the EU and EU members that are not in the Schengen zone.
unwillingness to curb economic immigration
Every ‘expat’ from the US, every Indian programmer, every EU citizen working in another EU country is an ‘economic immigrant’.
That has nothing to do with Lampedusa.
capitalist desire to maintain poverty wages
What are you on about? Those people aren’t even allowed to work.
The new arrivals are not properly integrated into their host society
Yes, they are kept in an overcrowded camp on a small Italian island.