Is there a practical difference in cost though? A Dutch insurer (Univé) used to do the same, but in practice there turned out to be no significant different in total amount of money spent by customers. Even though they gave their profit back to their customers at the end of the year, they couldn't compete on price.
One big non-profit player will drive all the prices down thanks to competition.
There is no reason for private insurance to be more expensive if they have non-profit competitor. If this competitor was to disappear, on the other hand, the costs would probably sky-rocket.
This is popular wisdom but experience show the opposite: for profit insurance companies tend to be less efficient. I am not sure what the reason behind is.
I pay 758 SEK per month now and with Länsförsäkringar I'd end up paying 968 SEK for the same coverage. I do have a 10% discount on my current insurance due to having several policies at the same company. That's still less than the difference though, so Länsförsäkringar would have to refund me around 1200 SEK per year to break even.
That would be around 10-15% of the entire yearly cost, and I don't think they can promise those kinds of refunds year over year.
There has to be since no shareholders are involved assuming the rest of the setup is the same. If they are not cheaper then it's more likely that the coop is badly run which sadly is not uncommon.
There's at least one other alternative. The NFP uses the excess to pay better wages across the board. Thus benefiting every community those wages are spent in, which will usually be local (both to the business and it's clients).
Monies move toward local, low cost and essential spending as opposed to remote, high cost and luxury spending that one would expect to dominate with dividends paid out by for profit businesses.
For me getting a home insurance for my rental apartment in Sweden, Länsförsäkringar in my region (They're split up in regions) was the cheapest one at the time I was looking.