Where a treaty-free battleship gun race would plateau

Without a successful Washington treaty, where would battleship size and gun-caliber escalation probably plateau?

Practical fleets would likely settle near 16- to 16.5-inch guns because their rate of fire and damage outperform slower giant weapons, while calibers above 20 inches would survive mainly as prestige projects.

Guns above 20 inches might appear as prestige projects, but the practical attraction of 16- or 16.5-inch weapons would remain strong. Before radar fire control, both sizes would fight at ranges limited by what could be seen. The smaller guns could send considerably more shells toward a target while the larger weapons reloaded. The discussion places 16.5 inches near the upper end of one loading-rate range, with roughly 17- to 20-inch weapons slower and still larger guns slower again. British willingness to trade some 8-inch cruisers for more 6-inch ships provides an analogy for choosing volume of fire. American super-heavy shells and possible British 16.5-inch Greenboy developments would also make shell quality part of the comparison.