VDI does not eliminate the necessity of DLP. The Data Loss Prevention (DLP) argument is one that is becoming relevant because of the public nature of most organizations and the penalties/damages associated with sensitive data breaches.
Recently enacted privacy regulations around breach disclosures have forced many organizations to rethink how they are securing sensitive data.
So it is recommended to use the same tactic as with physical desktops and provide granular security controls around VDI. For example, if Social Security numbers are getting transferred within a network against protocol, these types of systems can catch it and stop it from happening.