Echoing Matthew's response from another light: many markers have a concept of stratified predictive accuracy. In this sense they provide extremely good predictive accuracy in a subgroup or in-tandem with another marker. Two examples from the health sciences:
Suppose for instance two types of breast cancer grow in women who are premenopausal and post-menopausal. The majority of women who are diagnosed with cancer are post-menopausal, yet the cancers diagnosed in pre-menopausal women are extremely aggressive, difficult to treat, and their genetic markers are unknown. If you naively presume that all cancers have the same genotype and genetic markers, you will show a low predictive accuracy for a genetic marker that yields a 100% Area-Under-The ROC in premenopausal women.
Another example is how a dyad of conditions might be necessary for disease. For instance, in nephrology, people are typically at risk and subsequently are diagnosed with Stage 3 Chronic Kidney Disease once they develop both hypertension and diabetes. CKD is known to progress to ESRD, which required chronic renal replacement therapy, and is generally very bad. Interventions to halt progress of CKD are poorly known, so earlier diagnostics are needed, but the manifestations of the disease are coincident with many other conditions, it is only a specific spectrum of conditions or a combination of markers that may inform clinicians that the patient has CKD.
Just the same, a stepwise approach to evaluating a sequence of markers does not hold the promise of identifying an optimal ROC in any scientific sense, albeit perhaps in a statistical sense it would. In my experience of evaluating markers, the best use for ROC is evaluating a pre-specified hypothesis about a specific marker rather than a huge list thereof. The CIs for ROCs and their AUCs tend to be quite wide since they deal with empirical functions, and after correction for multiple testing, the risk of Type II error is just too high to justify evaluating 100 markers or more.
The exception to this might be the understanding that the nature of the analysis is a hypothesis generating study. That means, however, that none of the previously collected data may serve to confirm this hypothesis. A separate study must be done. Many clinicians are disheartened at how irreproducible results can be from such fishing expeditions.