I assume this is based on traditional payment patterns to the different suppliers - so traditionally, you paid your energy supplier at the end of the quarter, after you had used 3 months of supply. By paying by dd there is a benefit that the supplier gets the cash early (for months 1 & 2) and can do something with it (ie put it on deposit) - they pass this to you as a deduction to your bill.

Added to their funding benefit, an energy supplier that gets the cash up front sees you as a better credit risk - people who pay by dd tend to have better credit, hence they can also pass on the cost of not having to chase you for non payment (hence the discount you receive is better than what they could get by putting the money on deposit for the time period).

Traditionally insurance was paid up front for the year, hence if you pay monthly, to the provider, you are now paying in arrears, so they are at a cash flow deficit, which they charge you for and they may well pass on your 'credit' to a 3rd party, so effectively you are paying for a loan for the year - so you may be better shopping around and getting a bank loan for a year at a better rate than the rate the insurance company gives you that has additional financing costs built into it.

Why insurance companies work on the basis that they need premiums up front, but their costs in the form of claims will be paid throughout the year (or later still, some of us have no doubt found) I have no idea. Well, I assume their premium to claim (and hence profit) ratios assume full payment - as you will find if you make a claim mid year, you generally need to pay off the remaining balance for the year.