Why D-Day did not need another fast battleship

Would sending another fast battleship to D-Day have improved the operation?

No. The invasion already had enough British and American heavy-gun support, so the extra ship would have been a poor use of resources.

Neptune's problem was not a shortage of battleship-calibre firepower. Existing British battleships and American heavy support already covered the targets assigned to capital ships. A modern fast battleship could therefore contribute more in a theatre where its speed and combat power answered an unmet need.