Why can't a Queueable use an Iterator that comes from a Set?

Question

I saw some surprising behaviour when storing the iterator obtained from a Set<Id> as a member in a Queueable class. So, I wrote the following trivial Queueable class to investigate:

public class QueueableWithIterators implements Queueable {

    public static List<String> results = new List<String>();
    private Iterator<String> myIterator;

    public QueueableWithIterators(Iterator<String> myIterator) {
        this.myIterator = myIterator;
    }

    public void execute(QueueableContext param1) {
        results.add(myIterator.next());
        if(myIterator.hasNext()) {
            System.enqueueJob(this);
        }
    }
}

The idea is that this Queueable will exhaust the iterator, putting values onto a static list so that we can see the results in an Apex test.

Then I wrote a couple of tests:

@IsTest
private class QueueableWithIteratorsTest {

    @IsTest
    static void setVersion() {
        Test.startTest();
        System.enqueueJob(new QueueableWithIterators(new Set<String>{'a'}.iterator()));
        Test.stopTest();

        Assert.areEqual(1, QueueableWithIterators.results.size());
        Assert.areEqual('a', QueueableWithIterators.results[0]);
    }

    @IsTest
    static void listVersion() {
        Test.startTest();
        System.enqueueJob(new QueueableWithIterators(new List<String>{'a'}.iterator()));
        Test.stopTest();

        Assert.areEqual(1, QueueableWithIterators.results.size());
        Assert.areEqual('a', QueueableWithIterators.results[0]);
    }
}

Running these tests, the List version passes but the Set version fails. More than that, by looking at the code coverage state, we can see that the Set version doesn't even run the execute() method.

If I try to run this code in Anonymous Apex, the List version completes and the Set version job just gets stuck in Processing status and never runs.

This smells like a bug, but is it a known issue (I couldn't find it) or a misunderstanding on my part?

NB, This is running in a Spring 23 scratch org.