No, I want to make sure everybody has liability insurance to pay for expenses when they cause a wreck.
That's not the same thing as "no-fault."
"no-fault" implies that regardless of how the collision occurred, everyone pays for their own stuff. Like in parking lots.
See, that works in parking lots because it's often hard to determine who screwed up, especially considering how poorly some lots are marked.
It does not work that way on public streets, for lots of reasons. Namely because innocent parties who are harmed by the negligence of others shouldn't, per our legal system, be required to bear the burden of that other person's mistake.
A "no-fault" world would mean that if you were crossing an intersection and got t-boned by a drunk driver who failed to stop at the red light, your family would pay for your medical expenses, funeral, etc, and Drunk Moron would only have to pay for the damage to his own vehicle.