Yes, it is a multidimensional competition. Price is not the only variable. So is service when you make a claim (I've been "screwed over" twice when making car

Yes, it is a multidimensional competition. Price is not the only variable. So is service when you make a claim (I've been "screwed over" twice when making car insurance claims). And so is obfuscation of services provided. So is money spent on advertising. And lobbying. All insurance companies compete with a unique strategy on the mix of variables.