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There are a great many costs built into the system that this analysis won’t get you: mandatory useless ingredients, arbitrary standards, and pervasive regulations.

I worked in aerospace and know a bit about this. Say you want to make a missile. Well, you better have the paperwork for literally every component to show that the metal used in all of it originates from a foundry in one of a tiny handful of countries.

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That sounds superficially reasonable. The supply chain should be trustworthy and reliable.
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I agree. We want to expect competence at all levels of the private and especially public sectors, but we're only able to insist upon it in a few key areas (aerospace, medical devices, etc.)

It is funny to see the same story every time. It's all burdensome regulation by the nanny state until something goes very very wrong and the public wants answers NOW, at which point it's incompetent government getting led by the nose by monied interest groups and their public relations departments.

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This is exactly what happened with Brexit. Bunch of people voted to leave the burdensome EU regulation environment, then realised they quite liked workers rights so they don’t get fired in an instant, having food quality standards was actually pretty good to protect us from chickens filled with hormones and they didn’t want a bunch of infrastructure built in their back yard so environmental regulation was also quite useful.
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The unknowns of defense spending is a feature and not a bug - for defense contractors
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The us military has been a wealth transfer mechanism for decades.
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The real problem isn't the price of the missiles. I wouldn't even care about the price of the missiles if they actually worked. But Iran kicked our butts. We don't have air superiority, we cannot guarantee the shipping of oil through the straight of Hormuz, or anywhere else in that hemispheres, our bases and our aircraft carriers are useless.

I wanna know what they've been doing with our trillions of dollars, because it sure as heck wasn't making an effective military.

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They ate the money. They got really fat and slow.
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Ukrainian FP-5 Flamingo has 2x official Tomahawk range and payload and costs ~$600K to make with minimal margins.
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RTX, formerly Raytheon, has the same revenue and net income as PepsiCo. PepsiCo has a higher profit margin.

Most of these companies are public and you can find their stats.

A Tomahawk missile is $3.6 million because it uses specialty components, all made in small batches using very expensive American specialist labor. It's also staggeringly more capable than a drone, or a shahed. Those extra capabilities are enormously expensive, because they are hyper niche.

A single American Artillery Shell is $3000.

Meanwhile, your $150k surgery bill example is completely different. It's a fake number, made up to cause a process to generate an actual, intended price somewhere. Your insurer and the hospital play some insane game of chicken where the insurance promises only to pay a percentage of what they are billed and so the hospital submits a fake number to get what they actually want (or nowadays the system is even more byzantine)

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If you were to count the margin of everything it would be 100%. At the end of the day everything is either a resource harvested from the earth or human labor.
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The more common concept of margin used in this context is net profit after expenses, including labor expenses. The question is therefore roughly "How much is purely for capital profit taking rather than directly involved with compensating labor and purchasing materials?".
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Everything is human labor. There is no such thing as a “resource” without human labor to convert raw earth into something useful.
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Two things that are necessary are both necessary. That doesn’t mean one collapses into the other.
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IP at the margin?
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Everything is food and air. There is no such thing a "human labor" without food and air to sustain it. I'm not sure what your point is.
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Help me understand this.

There's the cost that the employees pocket, and then there's the share that the shareholders pocket, right? Doesn't "margin" represent the latter?

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100% of the money ends up going to people.

It’s not like you get to the end of the chain and trade a fistful of dollars with the ingot of aluminum itself.

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Sure, the concept of money is only meaningful / valuable to humans.

But isn't there a conceptual difference between the "owners" of the Tomahawk factory vs. the people who are actually putting the missiles together?

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I think most of the cost is in R&D
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Those margins are the cost of Capitalism.
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Many defense contracts are cost plus. https://en.wikipedia.org/wiki/Cost-plus_pricing
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Nope. Very few defense contacts are still issued on a cost-plus basis. Especially not those for serial production of existing munitions.
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