Why the US Navy retained all-gun heavy cruisers

Did the Soviet surface threat help keep US all-gun heavy cruisers in service into the 1970s?

Yes; the guns offered a reliable surface counter and gave the ships continuing value for diplomatic presence.

The Soviet cruiser threat gave the US Navy a reason to retain heavy cruisers with a substantial gun battery. Large guns offered a dependable way to counter an opposing surface ship. The same armament also had value on peacetime presence missions. A visibly powerful gunship could command diplomatic attention, so its usefulness extended beyond the prospect of fighting Soviet cruisers.