Yes of course someone pays for it, in this case your deductions as you say. But I think there is a fundemental difference to employers paying for health insurance in that it doesn't depend on your job. So if you lose your job you don't lose your healthcare so companies can't use that as a way to retain you.

And the actual cost of healthcare to the organisations paying for it is actually far lower than the US system, probably partly because it's more regulated and also because there is far less litigation so insuranace for doctors is cheaper.

So I don't think the US system is "more efficient", unless by "efficient" you mean in extracting money from patients / their insurances. In the US hospitals exist to make money, in the EU it's more about providing treatment.