And I don't think that "ceases to have a useful meaning". I think it just doesn't let you argue that your system is better based on absence of "coercion".
Do you or do you not believe that doctors in the UK are coercing the government by demanding a fair salary in exchange for the lifesaving services they provide?
I don't think it's necessarily limited to that, but I do think all such situations are coercive. Whether someone is having a gun pointed at them, or being denied healthcare, they are being coerced. That said, I do think most coercion does ultimately amount to the threat of death or suffering, even if it becomes very indirect in practice.
>Do you or do you not believe that doctors in the UK are coercing the government by demanding a fair salary in exchange for the lifesaving services they provide?
Trying to evaluate the actions of individuals in a wider system is not very helpful. Are the doctors being coercive? Yes. But they're also being coerced in turn by the individuals they rely on for survival (i.e. the people they buy food from) so it's hard to ascribe blame. It's the system as a whole which is coercive.
And this is my point. Both market based healthcare and state provided healthcare rely on coercion to function, so you can't distinguish them morally on that basis.
The only hypothetical system I know of that would actually be free of coercion would by something like anarcho-communism, where people have free access to the means of survival, and it is produced by people's free choice to work for the benefit of others. But I'd guess you think such a system wouldn't work.
Can you honestly not see the moral distinction between me intentionally shooting you with a gun and me not applying first aid after someone else has intentionally shot you with a gun?