I largely agree, but I'd argue that Light did have a political theory and societal sea change in mind.
The theory was fascism, the change was he'd make everybody too afraid to commit a crime because he was sitting in the Panopticon control room. Kira is supposed to be the ultimate Big Brother, everywhere and nowhere, enforcing his will, and above all else concentrating the power solely in his own hands.
And that's really the danger of the death note, that fascism is basically pre-installed. Your sole tool is murder, and while that gives you temporary perfect control it is also the only carrot or stick you have at your disposal. The rewards you can give are either withholding murder or eliminating somebody another party wants dead.
The entirety of your authority and power rests on use of lethal force and you can't even fully monopolize it. Other people can kill folks you want alive and even get away with it.
If you just treat the thing like the world's best most amazing sniper rifle or a network of assassins you can absolutely use it to aid a cause and effect positive change, but the instant you make it a load bearing element of a political system you're gonna be down to fascism sooner or later.