There is massive competition in the auto insurance industry. I was about to say that this would imply that profits wouldn't go up because folks would save 10% by switching to GEICO.
However, I realized a problem.
Currently, all insurers are looking at the same demographic data. If this scheme is put into practice, then insurers will have a proprietary information on an individuals' driving habits, letting them offer discounts to good drivers. This leads to a situation where to switch to a different insurer will always cost more for a good driver, so few drivers will switch. This means that trying to switch insurers will become a signal of bad driving, so insurers will charge more to new customers. This leads to fewer and fewer people switching insurance companies, leading to decreased competition.
In practice, it's the opposite. Switching may be a sign that you are a bad driver but it's also a sign that you are price sensitive which is usually the more important signal. Never switch and you are flagged as price insensitive and therefore a fine candidate for being over-charged.
One solution would be to have laws like Europe has that require companies to provide to each customer all data it's collected about that customer on request Then you could "take your data with you" and show you're a save driver.
Interestingly enough, Geico was started by someone who successfully predicted that government employees would be less risky (the GE stands for Government Employees):
Unless you have access to your own data. Perhaps the insurance companies could be forced to share it upon user request, for example. Then the new company knows everything the old one did.
However, I realized a problem.
Currently, all insurers are looking at the same demographic data. If this scheme is put into practice, then insurers will have a proprietary information on an individuals' driving habits, letting them offer discounts to good drivers. This leads to a situation where to switch to a different insurer will always cost more for a good driver, so few drivers will switch. This means that trying to switch insurers will become a signal of bad driving, so insurers will charge more to new customers. This leads to fewer and fewer people switching insurance companies, leading to decreased competition.