It was only the German position against the American trench gun in WW1, but never wide agreement:

On September 15, 1918, the German government officially protested the use of the shotgun in a note verbale—an unsigned diplomatic note—transmitted to the Spanish Embassy in Berlin, then to the Swiss Embassy, and eventually to the American legation in Berne, Switzerland. The note asserted that the use of shotguns by U.S. forces violated Article 23(e) of the 1899 and 1907 Hague Conventions and warned that any American captured with a shotgun or shotgun ammunition would be executed.
[...]
In his formal response to Germany’s protest, Secretary of State Lansing maintained that the shotgun the army used could not be the subject of “legitimate or reasonable protest” under the Hague Conventions.
[...]
In the 100 years since the protest, the U.S. government’s position with respect to the use of shotguns in wartime has never wavered. U.S. military forces used shotguns in World War II, the Korean War, the Vietnam War, and even in post-invasion Iraq (to clear out suspected insurgent hideouts in house-to-house fighting).

Source

I don’t disagree. However, definitely not a war crime.

Source: was infantry.

Tangentially, I disagree with your .45 or 10mm as well. Ballistics have come a long way and unless you need to defend from bears, the 9mm is wonderful, lighter, cheaper, and has a higher carry capacity.