The Danae class reflected tonnage and role constraints

Could retaining and rearming older destroyers have avoided the need for the Danae-class light cruisers?

Not simply; the Danaes used available tonnage for a familiar light-cruiser requirement, though more destroyers might have freed cruiser tonnage for a larger type.

Retaining older destroyers might have changed the requirement that produced the Danae-class light cruisers. The Danaes answered the tonnage, tasks, and design knowledge available at the time. The Royal Navy chose a light cruiser because it understood that type and believed it would meet the need. More destroyers might have covered smaller tasks and freed cruiser tonnage for a larger ship, but that would have required a different force-structure decision.