Why Alaska paid so much displacement for speed

Why was Alaska so lightly protected for her tonnage, and would a 30- or 31-knot design have achieved more?

High speed imposed an exponential machinery and hull penalty; a slower ship could save weight, but design growth would still consume much of the theoretical margin.

The Iowa and South Dakota comparison shows that six additional knots demanded roughly 82,000 more shaft horsepower. The larger machinery plant also needed a longer hull and its own armour, multiplying the displacement penalty. Alaska studies estimated about 37,600 tons for 30 knots and 39,300 tons for 33 knots before design growth drove the faster concept toward 45,000 tons. Reducing speed would save weight, but it would not magically produce battleship protection and armament on cruiser displacement.