But if no-fault is such a great idea, why not voluntarily agree to it? Your agreement with your insurance company could specify that should you get into an accident with someone who has made a similar matching agreement with their insurance company, then the no-fault rules will apply, and perhaps you would get some higher coverage. The insurance companies could then make agreements regarding no-fault coverage between their clients, agreeing either pair-wise or in larger negotiations. My law professor here tells me he knows of no reason why such contracts wouldn't be upheld in court.
Given that those who think no-fault is better could obtain its benefits voluntarily, it is not clear why they should want to impose it on the rest of us. If insurance companies thought it would save them money, they should offer lower prices for such no-fault contracts. Perhaps they have an "adverse selection" argument in mind, where people with high risks are more likely to buy such no-fault contracts, and so they couldn't be offered at a lower price.