But most people do self insure most risks that are as small as $10k. The most popular forms of insurance are for risks that are much larger and could not easily be self-insured.
For instance, with home insurance, the potential risk would be hundreds of thousands of dollars to replace a house that was entirely destroyed. With health insurance the potential risk is millions of dollars to treat something like cancer. With car insurance, the potential risk is hundreds of thousands of dollars of liability if you injure someone. You can't exactly expect someone to keep millions of dollar lying around to cover the possibility that they get cancer or their house burns down.
For instance, with home insurance, the potential risk would be hundreds of thousands of dollars to replace a house that was entirely destroyed. With health insurance the potential risk is millions of dollars to treat something like cancer. With car insurance, the potential risk is hundreds of thousands of dollars of liability if you injure someone. You can't exactly expect someone to keep millions of dollar lying around to cover the possibility that they get cancer or their house burns down.