EU member states do still issue their own national passports although they do not need them to travel within the EU. Outside the EU I am sure there are certain advantages for diplomatic and business purposes because the EU is made up of both respected and rich western countries like Germany and former Soviet states like Romania. Within the EU itself the main reason is probably political. The passport is probably one of the last remaining symbols of national identity for EU member states, especially those which have joined the euro and people still like some kind of symbol of national identity.
More than 2,000 migrants threaten to break out of Hungarian camp (Reuters)
from the article: Fear is driving Israelis to obtain foreign passports