There's something I'm still not getting. Car insurance should not have a significant lag because the probability of claim is not related to the date of policy. I'm just as likely to get in an accident on day 1 of my policy as day 1,000.

If daily claims meet or exceed the daily premium, the only time available to earn interest is between premium receipt and claim payment.

Imagine founding an insurance company and on day one you receive $100 in premiums and $100 in claims.