All the people they lost against still suffered devastatingly while the American citizen was just fine and dandy. They fought a lot and materially and human cost wise lost quite a bit more in comparison. America hust didnt get what it wanted after killing all those people. They can force a vert pyrric victory

Sun Tzu's whole thing for that is basically, before you decide to go to war, make sure you understand exactly what you are trying to achieve first. Which is literally basic effective project management tactics in a nutshell.

If you can achieve that objective without ever having to field soldiers, then you should always achieve it without fielding soldiers. As well, fighting simply to fight is not a good enough reason, as you will usually lose to the defender's advantage, even if you have vastly superior numbers and technology. It is better to use the threat of overwhelming force to force your opposition to do something than actually test it, as warfare can be extremely unpredictable, like casting dice on a craps table. Moreover, any amount of damage you sustain, even if you are victorious, leaves you vulnerable to a third party who did not participate in the conflict.

The annals of history are littered with the corpses of empires who defeated their primary political opposition in war, only to lose to a player that wasn't even considering playing the board until the other two players had weakened themselves.