As transparency grows, fewer and fewer companies are going to get away with leaving their current customers at higher rates while they chase new customers.
Loyalty is about submission, and companies will have to figure out how to give up something they want (new customers at any cost) to keep the customers they have. It's only fair.

Time: Proof that Loyalty is for Suckers, 2012-Sep-6, by Brad Tuttle

A new report from the Texas Office of Public Insurance Counsel estimates that a driver who has been with the same auto insurer for eight years would save an average of 19% on premiums by switching providers.

The study notes that nearly 60% of drivers rarely or never shop around for auto insurance policies, and that, for a variety of reasons, less than 10% say they’re likely to switch insurers.