Why the alternative design has a lightly armoured conning tower

Was the very light conning-tower armour an error in the alternative battleship design?

No. The design keeps it light because heavily armoured conning towers are considered a poor use of protection weight.

The design's roughly two-inch conning-tower protection is intentional. Heavily armoured conning towers are treated here as a poor use of armour weight. Royal Navy admirals often preferred other command positions, and conning towers could become storage spaces. The decision exposes a specific protection trade-off inside the larger counterfactual instead of treating every historical armour feature as mandatory.