Inject logger by CDI, an anti-pattern?

Looking at this code:

@Stateless
public class AStatelessEJB {

@Inject
private Logger logger;

(...)

Why a logger, which is typically final and static, is injected by CDI into a stateless EJB (as an instance variable)?

Is there any advantage? Or only disadvantages such as:

• overhead of CDI lookup (per each bean initialization)
• overhead of CDI initialization (per each bean initialization)
• overhead of CDI injection (per each bean initialization)
• overhead of garbage collector clean up (each time the bean gets destroyed)