It's not though. The US has been getting compensated for its military investment all around the world.
The explicit architecture of the petrodollar system is that the US will protect international shipping, and in return all petroleum contracts will be priced and executed in dollars. This makes the USD the international reserve currency, and every country participating in international trade needs to hold USD.
How can they put those USD to work? By buying up safe US government debt and other financial instruments.
The US has been rewarded with near unlimited borrowing ability assuming it remained the most stable, powerful, and trusted partner. We could use that to fund practically any investment we want.
> that the US will protect international shipping, and in return all petroleum contracts will be priced and executed in dollars
People say this, but the dollar is free-floating against other currencies and oil is priced on (OPEC-manipulated) supply and demand, so it seems like an accounting fiction. Like, we could price oil in pork belly futures.
Yes but they are settled in dollars, and all the countries of the world are in fact holding dollar reserves.