Sometimes people are forced to buy insurance. In the UK it is mandatory to have car insurance (else the police will literally take away and crush your car). My mortgage demands that I take out home insurance. And of course the state provides a kind of health and unemployment insurance which is mandatory for UK taxpayers.
In many (most?) jurisdictions you can post a bond for liability insurance. This is typically used by fleet managers etc, but is also available to HNW individuals.
Essentially you prove to an insurer (by posting a bond) that you can and will pay for any third party damage you cause, and in return they give you a practically free (or cheap, super-high-deductible) policy.
In the UK you can post a bond in lieu of having motor insurance, but it's something like £250,000 so rather out of the range of the ordinary car driver. (It's mainly used for commercial vehicle fleets as you say.)
You aren't forced to have savings.