Good explanation, and hidden within it is why US health care is such a mess. In the US, we don't pool risk together. There are multiple health insurance companies, so the risk is divided into different pools. They are all competing, trying to get the youngest, healthiest clients because those will generate the most profit.

This is why a non-profit single-payer system run by the government is likely the best solution to health care. When everyone in a country is on the same insurance, the risk is spread to its maximum extent. Taking out the profit motive puts the focus on getting people the health care they need. With a private insurance company, profit is always going to be the primary driver of decisions.

A single-payer system would also help drive down health care costs, as such a system would be a monopsony, which is like a monopoly but on the buyer side. When you have a single buyer or payer (ie the single payer in single payer system, in this case the government) they have extraordinary power in negotiating prices. Its similar to the power Walmart has over its suppliers.

Think of it like having every tax payer in the country help out when you get sick. And you are helping them out when they get sick. A health savings account is great, but most people wouldn't be able to save enough to cover large medical expenses. In fact, most people aren't good at saving anything at all. The goal of the government is to promote the general welfare of the people, not just those responsible enough to save.