Why modern navies understate ship classes

Are battleship and frigate labels used because they are easier to sell politically than cruiser and destroyer labels?

Yes; many modern frigates and destroyers are functionally specialized cruisers despite their labels.

Many large frigates are described as cruisers optimized for anti-submarine warfare. Modern destroyers similarly resemble cruisers specialized for air defense, while the largest ships combine several warfare areas. Their peacetime work, including independent deployment, presence, and diplomacy, also follows the traditional cruising role. Political presentation encourages smaller-sounding labels even when size and mission breadth point toward cruiser classification.