There's inefficiency in any system. Engines, motors, fusion power, and transistors. We can calculate their efficiency, and the numbers aren't impressive if that's all you care about. Maybe it's better to ask how they compare to other methods of doing work. This is the cost of the system, and it's either worth it or it isn't.
The US medical system is a public-private partnership, and it's likely the most expensive system in the world for what the benefits it provides (see "List of countries by total health expenditure per capita" on Wikipedia). The government can only optimize here if it's willing to rein in the for-profit middlemen.
To paraphrase a quote, I'd be tempted to call an obsession with efficiency a hobgoblin of little minds. Or maybe it's just an excuse to cut programs.
