One, because wealthy people sometimes want 'dual citizenship' (which has to be kept a secret in the U.S.) because they feel like if things fall apart in one country, they can quickly escape to another.
Two, some business transactions require citizenship.
Three, some rights are only available with citizenship.
Citizens of "poor" countries have great difficulty traveling internationally, even if they are personally wealthy. (Other countries may not grant them visas to enter, and may mistreat them at border crossings.) Maybe their home country isn't a very attractive or safe place to live any more. Etc. etc.
There are alot of very rich people in countries with undemocratic governments, who would love to move to europe. Think the Middle East, India, China, ...
EU is not an asylum for criminals (actually is a terrible place for a criminal trying to secure his freedom, because it takes only one country to raise an 'european arrest warrant' afaik), for that reason mobsters are more likely settle in countries without extradition treaties to their country of activity, or some banana republic where it's easy to vanish.
