Maybe not the government or citizens, but war helps the congress members, the CEOs of the military industrial complex, and their families get fabulously wealthy.
The government isn't something that exists above society, but is a facet of it. The MIC directly profits from wars, it pays politicians, politicians are motivated toward hawkish positions, the taxpayer is made to subsidize this. There are many other circuits discussed in the article, as concern the impact war has on the consumer market, how it's used for imperialism, etc.
Ultimately, wealth comes from labor, but the arrangement of war profiteering is extremely good at extracting wealth from labor in all sorts of ways.
Wars are plenty profitable if you’re a lot bigger than your opponents and can force them to be subservient to your business interests. It’s not a fluke that the richest country on earth is also the one with the most frequent wars.
Is that not the point? Government functions by moving wealth from the public into the private, massive expenses portrayed to be for our benefit end up being excuses for taxes, and the enormous costs facilitate enormous wealth transfers into the private corporations who support and facilitate the wars.
That's a side effect of capitalism and lobbying (aka bribing) the government for preferential treatment. But it's kind of the opposite of the point of government. Most businesses are incredibly selfish and will cut every corner they can without the government there to enforce workplace safety, market rules, and policing fraud and theft.
I don't care for capitalism, but Adam Smith was an abolitionist. He absolutely hated slavery because he believed it to be immoral firstly, and economically inefficient secondly. He couldn't prove the second part, but once someone at either Cambridge or Oxford did manage to prove it, Great Britain and Europe outlawed slavery. Again, I'm not defending capitalism here, and I'm certain, from the tone of The Theory of Moral Sentiments, that, were he alive today, Smith would be railing against Capitalism. I'm just pointing out that it was supposed to be abolished far quicker than The Civil War.