Certainly one can kill their way to victory in war, it just depends on what type of victory one seeks.

But if the war is an internal one, this is likely to be a pyrrhic victory.

The "American Way of War" remains a valid model for state on state warfare. Defeat the military, government and population of one's opponent completely; and then be generous in peace with broad reconciliation in peace, avoiding overly corrupting the perceived self-determination of the new governance that emerges, and remember that the defeated state will tolerate much more "influence" over their future if one is perceived as lessor of two evils (i.e., US presence in Germany, South Korea and Japan prevented much harsher occupations from impacting those places and people. We tend to forget that).

When one stops the war when the opposing government capitulates, but their military and population are not defeated, it is still a win, but not one that validates treating the affected nation and people as "defeated" (i.e., Germany post WWI, and equally Russia post-Cold War).

What Luttwak advocated for in "Give War a Chance" was the importance of letting political conflicts play out. When an external power intervenes to force a winner through the application of their power, it corrupts the legitimacy of the victory. The loser will always rationalize "but for...". This is when external power comes in as arbitrator. I believe increasingly external power should come in as mediator. Not to pick winners and losers; but to use their power to force the internal parties to the table and address issues that the current government would prefer to ignore. Like mediation in a failing marriage, terms developed and agreed to by the parties are more palatable and durable than those imposed by a judge.

The nature of war is not much changed by the modern strategic environment, but as power shifts to populations relative to governments it is highlighting that political conflict within a single system is not the same as that between two or more systems. War is the final argument of Kings; but revolution is the final vote of the people.