MWI does make empirical predictions. E.g.: 'No Collapse interpretation will be empirically supported.' Thus far this prediction has been vindicated, even though Collapse interpretations, as a group, are verifiable. Of course, MWI has to share this glory with other alternatives to Collapse; but that's at best a reason to dismiss arguments between MWI and Bohmian Mechanics, not a reason to dismiss arguments between MWI and Collapse.

As for Heisenberg-style Copenhagenists... if you think it makes no difference whether we accept or deny their view, then it would seem most consistent to also consider it a matter of indifference whether we affirm, deny, or remain agnostic regarding the doctrine of Solipsism. And I don't think that's tenable; our experiences provide experiential evidence against the supposition that there's no reality transcending our immediate experience.