Yugoslavia didn't have centralized planning for products, one could even argue it had a meritocratic natural selection (sort of) and there still were shortages.

Maybe the EU as a whole could pull off being 'fully independent' but it would require way more collaboration between countries than what we currently have.

And, compared to USSR, Yugos production was much higher quality and shortages were much smaller.

EU could become fully independent by simply taxing imports. Designated collaboration between countries would just lead to inefficient central planning style stuff. Which is how many trans-Europe projects died