When unprotected cruisers made strategic sense

Would an unprotected cruiser be worth building?

Yes for low-threat policing and presence roles, especially when low cost buys enough hulls to sustain availability, but not as a peer-war fighting ship.

Unprotected cruisers were poor choices for peer fleet combat, but they could serve in piracy suppression, anti-slavery patrols, colonial policing, and showing the flag. Those missions demanded range, presence, and numbers more often than the ability to exchange heavy fire. Three cheaper hulls might keep one ship continuously on station when two more costly protected cruisers were both unavailable for repair or refit. Force readiness depended on the number of ships available, not the specifications of a single hull. An unprotected cruiser could therefore be sensible when its role and likely opposition were tightly defined.