Of course not, but people may complain that none of them are from their country. Maybe someone from Spain would like to see Picasso or some other famous Spanish figure in there. That's the reason for using generic images, the EU and the Eurozone in particular is a trade alliance of countries with different cultures.
I like what they did with coins the best, where one face is common, showing a map of Europe, and the other is free for the issuing country to choose from. I like the message it delivers, different cultures, united. And as people travel, they will bring coins from their countries, the resulting effect is that if you go to a Eurozone country, you are likely to see coins in circulation from all over Europe, which is a concrete example of free trade happening.
I wish they did the same for banknotes: one side generic, one side country-specific, but it may be impractical.