None of that precludes that some parts of that structure to be private. You just need to have a structure that is resilient to non-compliance.
So I actually agree with you: if the United States want to use mercenaries, they should improve how they do it. But then again, there might be a way to do it that works.
I do not think this is practical or even desirable.
Instead, more and more, the US is trying to become a world government, with 6.7 billion people affected by their choices, indirectly taxed by their choices (US corps replacing local companies and transporting the profit out of the country), without any representation.
This is a very unbalanced situation, and is just asking for a revolution. Which will end up making life worse for almost everyone.
We need a fair world government if we want to do these things, and that means representation of all people.
Obviously, the US, which would lose the most from this, objects.
Or the weakness of those countries towards US that can be explained by recent history.
Until next war.
So if there is a need for these forces, they need to be a lot more open about their operations with the government. With more oversight then even the regular troops and accountability up to CEO level of the company for actions performed by their armies.