Why Scharnhorst carried 11-inch guns

Did Scharnhorst and Gneisenau carry 11-inch guns because of politics rather than doctrine?

Yes in an indirect sense: Versailles-era industrial destruction left 11-inch weapons as the largest practical guns available when the hulls were built.

The explanation for Scharnhorst and Gneisenau's 11-inch guns is Germany's limited ability to manufacture larger weapons when the ships were built. Versailles had severely reduced the relevant armaments industry. The navy therefore faced a choice between fitting the available guns and leaving the hulls waiting for armament. Politics affected the design through the industrial capacity available to its builders.