Even though they'll take responsibility, in every state in the US you must still have liability coverage. If these companies are to be their own underwriters so to speak then they'd have to jump through hurdles to be approved to operate as an insurance company as well. They could obviously partner with insurance companies as well.
In many states, you do not need insurance, but proof of financial security which can be a surety bond with the DMV. In my state it's only $50,000. The company I work for does this and we are in no way associated with or approved as an Insurance Company.