Why World War One did not invalidate every armored cruiser

Did wartime armored-cruiser losses prove that the type was inherently a death trap?

No. They proved that old armored cruisers were obsolete; a modern, larger continuation could still fill valuable roles.

World War One demonstrated the vulnerability of old armored cruisers in battles they were not designed or prepared to fight, not the impossibility of the category. Continued development could have produced modern ships of roughly 15,000 to 18,000 tons with far better protection and machinery. A squadron of those cruisers, reinforced by battlecruisers, could perform the shallow-water offensive role envisioned for the large light battlecruisers. Their existence might therefore remove the requirement for Courageous, Glorious, and Furious in their historical form.