Why 11-inch guns did not solve the Deutschland class problem

Would an earlier-style armour distribution have materially improved the Deutschland class?

No. Their deeper problem was a small battery of 11-inch guns that lacked both cruiser-combat rate of fire and sufficient power against larger capital ships.

Machinery and armament mattered more than armour distribution for the Deutschland class. Its few 11-inch guns delivered neither the rapid fire needed in cruiser combat nor enough weight of fire to confront battlecruisers and battleships. In this assessment, the calibre worked partly as a status symbol whose visual impressiveness did not compensate for the battery's tactical limits. Widespread 12-inch cruiser construction would also make a new 14-inch battleship look nationally embarrassing, so the apparent niche for an 11-inch cruiser would not remain stable. Role definition controls the answer: an impressive calibre can be a poor trade when a ship cannot excel at cruiser fighting or capital-ship combat.