How the G3 and N3 designs influenced later battleships

Why did the G3 and N3 designs have more impact on battleship construction than the Kii and Number 13 designs?

Their main influence ran through the research inherited by Nelson and Rodney, while Japan expected its own designs to provoke counterbuilding rather than overturn the naval balance by themselves.

The G3 and N3 designs did not independently reshape foreign battleship construction. Their durable influence came through the research behind them and the building of Nelson and Rodney, while G3 remains especially discussable because construction actually began. A later follow-up adds that Japanese planning for the Kii and Number 13 designs assumed British and American responses and matching industrial growth rather than a one-sided Dreadnought-style reset.