Why ten-inch naval guns miss the useful calibre steps

Would an automatic ten-inch gun be an effective compromise for a modern large warship?

It is an unattractive compromise in this comparison: much of a twelve-inch system's machinery and weight, less shell impact, and no 9.2-inch rate-of-fire advantage.

Above a certain shell weight, naval guns require heavy loading machinery that limits their firing cycle. In this comparison, broadly similar rates of fire extend across a range approaching ten to fourteen inches, although the range depends on the period studied and lacks recent comprehensive comparisons. A ten-inch gun therefore loses the rate-of-fire advantage of 9.2 inches while falling short of a twelve-inch shell's impact. It can carry much of the larger installation's cost and weight without either advantage. The eight-inch cruiser limit is explained as a Washington Treaty choice just above the 7.5-inch armament of Britain's recently built cruisers. That treaty history does not establish eight inches as the most efficient engineering choice. The rarity of ten-inch guns is attributed to the same problem of fit: they offer limited rapid-fire value for cruisers and less shell effect than most battleships require.