When you're driving someone else's car, their collision/comprehensive insurance covers damage to their car (although there's a chance their insurance company will decline to pay or decide to sue you depending on the circumstances). Your liability insurance covers personal injury and property damage that you cause to others.
Drivers are listed for two reasons. The first is because a big chunk of car insurance is liability insurance. The second is because the probability of the insurance company having to pay to repair or replace your car depends on the likelihood one of the drivers will cause an accident.
This is all made more complicated by the fact that personal injury lawsuits are a numbers game. If the driver didn't have insurance and their estate has very little money, it doesn't matter that making them liable is a slam dunk case. It's not worth the effort. On the other hand, if the car owner has insurance, is alive, and has a lifetime income potential in the tens of millions of dollars, that's worth a lawsuit even if the probability of success is lower.
It feels scummy, but most personal injury lawyers are investing in cases. They'll be happy to take a lower probability chance on a bigger return. It's not all that different from venture capital, although you could argue pretty easily that VCs are a more positive force for social good and value creation.
