Secondary batteries stop screen breakthroughs

Could the need for cruiser escorts justify removing battleships' secondary guns?

No. Secondary guns defend against destroyers that penetrate the cruiser screen while the main battery engages larger targets.

A battleship's cruiser screen is supposed to stop torpedo craft before they reach the battle line, but designers cannot assume that every interception will succeed. Secondary guns give the capital ship a last defensive layer against destroyers that break through. The main battery is normally reserved for enemy battleships and other valuable targets because using it against small, fast attackers wastes heavy fire and attention. Cruisers occupy an awkward middle ground: they may draw main-battery fire when exposed, whereas destroyers are primarily the problem the secondary battery is meant to solve.