Please point me to this law. Unless you are in a mortgage, no law requires you to hold homeowner’s insurance, and you can absolutely self-insure, to my knowledge.
The same is not true for auto insurance in most states, though most also have an option to self-insure by putting up collateral.
There may not be a law explicitly stating you have to have homeowner's insurance. But.
Without such insurance, specifically the "injury liability type" with its limits; then if someone gets injured on your property there may be no limit to your liability.
So even people who could afford the loss buy insurance because it is the best method of limiting intangible risks.
My understanding is that for an LLC to provide protection the house would have to be used for purely business purposes and that there can be no co-mingling of personal finances. the concept is called "piercing the corporate veil". IANAL but I looked into this pretty extensively when choosing how to protect myself with investment properties.
The same is not true for auto insurance in most states, though most also have an option to self-insure by putting up collateral.