For this analysis to make sense, we need to deconstruct "auto insurance" into its various parts, because this will matter. Note that some jurisdictions have no insurance requirements (eg New Hampshire) and others have a thing that splits bodily injury across all parties, meaning that the liability component is harder to apportion. The point is that the analysis will vary slightly based on where you are.

Typical auto insurance can include: third-party liability (the component mandated by most US States), collision, comprehensive, medical, and uninsured/underinsured motorist. These are all insurances that you buy, but they might not necessarily pay out to you.

Third-party liability covers damage or injuries that you cause to some other party, payable to that other party on your behalf. Crashing into a lamp post, a pedestrian, or an occupied car all will be paid from the third-party liability coverage limits. A state like California mandates a minimum coverage, but it's not been updated for inflation and stands at a paltry $30,000 per person injured and $15,000 for damaged property.

Collision insurance covers your automobile as it is being driven. So if you wrap your car around a telephone pole, this insurance pays to replace your car for you. Generally, this insurance follows the car, so if you lend the car to a friend and they crash it, the policy will still pay out so you can replace your wrecked car.

Comprehensive insurance is similar to collision, in that it covers your car. But notably, it covers the car when not in operation. So if a tree falls on the parked car, or someone keys your car, then comprehensive insurance will pay out. A rule of thumb is that collision applies if someone is in the driver's seat, and if not, then comprehensive would apply. Note that some states (eg California) explicitly exclude collision/comprehensive coverage for instances of hit-and-run where the assailant remains unidentified; this is a public policy choice, so that insurance prices don't skyrocket if anyone can claim that their mailbox-sized dent was due to a hit-and-run.

Medical insurance covers you and your passengers in the event of a collision for any reason. If you crash into a tree and it injures a passenger, your medical insurance pays out for their injuries. If a big rig pushes your car off the highway, then both your medical or their third-party liability can pay for your injuries. The oddity is that if you have health insurance, then auto medical insurance only pays for your deductible. That is, health insurance pays first, and anything that still remains can be paid by someone else's third-party liability (if available) or your own auto medical insurance. For this reason, some people omit auto medical if they already have health insurance, and can manage their deductible.

Finally, UM/UIM is a policy that, oddly, covers other people but pays to you. Imagine being struck as a pedestrian by a teenager riding a e-moto without a license or insurance. If you were struck by a motorist, their third-party insurance would have paid out. But here is an underage motorcyclist that doesn't have any insurance at all, despite a legal requirement to have insurance. To prevent you from being SOL, your UM/UIM stands in for their lack of third-party insurance, meaning it will pay you for all your injuries and damages.

With all that background, let's return to the titular question. Supposing a ludicrously expensive car is now on the road, and the owner has purchased every policy above for themselves, there really shouldn't be an impact to other people's insurance rates.

Third-party liability is based on one's propensity to incur damage or injury to other people. The motorist driving in a sea of econoboxes is not somehow more disposed to causing a collision if they're instead driving in a sea of expensive cars. The amount of damage might go up, but third-party liability is always written with a max coverage limit anyway.

For collision and comprehensive, these are based on the value of your car, not other people's. So it really shouldn't go up, at least directly. Of course, there are second-order effects, such as if billion-dollar cars cause mechanics to move away from servicing normie cars and towards servicing only these luxury cars, causing reduce supply of mechanics and thus inflation of the cost to repair all cars. That would indeed increase the payout for collision and comprehensive insurance, which would increase everyone's rates.

Medical insurance is also fairly unchanged, because it either covers your bodily injuries (which could be high but not infinity) or is capped by your health insruance's deductible (which post-ACA is indeed limited). A billion-dollar car causes injury under the same physics as a normally-priced Honda Civic. It's not like the billion-dollar car weighs 30,000 kg, right?

And finally, UM/UIM is about uninsured motorists or motorists with not enough insurance. Rich people have deep pockets to cover any injuries or damages which their third-party insurance doesn't cover. So all else equal, ludicrously expensive cars on the road doesn't move the needle for other people here.

Overall, auto insurance tends to internalize the individual costs of automobile risks, so that there is no direct spillover onto other parties. But even while the auto insurance market is efficient, the market of new and used car parts is not. The market of healthcare in the USA is not. The market of feasible alternatives to driving is not. While a billion-dollar car doesn't disrupt this careful balance within auto insurance, so many other things will.