I can think of a couple of very recognisable Insurers (at least in the UK) that have striven to define themselves on the value of their offering, rather than purely on price. In order to raise awareness of this they have invested heavily in the development of their Brand (and I have been told by a number of highly successful professional Marketeers that there are very few recognisable brands in Insurance - and I'm not counting aggregators).
Although the article I have highlighted is more focused towards Commercial Insurance, and was written in 2008, the message is strong: Help the customer to better understand their risk, and then provide an appropriate means for them to transfer that risk.
Helping the customer / society to better understand and manage the risks they face is the raison d'etre of insurance. It seems though, that it is the disruptors that are working to promote this more than the existing players.
Insurance buying decisions should be made based on the net impact to the business (....) The considerations, in priority order, are the following. What is the potential balance sheet impact from an adverse event? What are the cash requirements? What is the cost of the protection? Some of the important related issues are: customer continuity; the organization's cost of capital, as well as determining if it is a net investor or net borrower; and the insurance protection being obtained relative to the cost. If the cost of insurance is too great relative to the risks being transferred, then why buy it? Just because goods or services are "on sale" does not mean that a buyer has a need for the price-driven offer.