When you wrap a Spring bean in a Sakai quartz jobs scheduler wrapper so that you can execute it there are 2 wrappers you can use. One is the standard one org.sakaiproject.component.app.scheduler.jobs.SpringJobBeanWrapper and the other tells quartz that only one copy of the job can be run across the cluster at once and the job map should be persisted between runs: org.sakaiproject.component.app.scheduler.jobs.SpringStatefulJobBeanWrapper
You don't have to implement the StatefulJob at all in any Sakai jobs because as long as you use the correct wrapper it will all just work, however lots of Sakai jobs do implement it as it makes the intention of the code clearer. It also will be picked up by quartz when we drop the wrappers.
Locally we had an instance where we didn't use the correct wrapper for a stateful jobs and one way to catch this is to have the standard wrapper warn if it's running a stateful job.