A comment on the previous post indicated the reader's willingness to include good service in his insurance purchase decision. A common sentiment that might make insurance companies think about emphasising good service in their marketing.
The problem is I'm not sure you can actively market good service.
You can make all the claims you like backed up with all the data you like but for claims to have real impact they have to be provable.
To make claims before purchase is to court sceptisicm and to risk disappointed customers. To make claims afterwards is to risk disbelief - be it of the relevance of the tiny survey samples so evident in beauty product advertising or be it the viewers' questioning of your vague definitions of satisfaction.
No, I'm not sure you can market customer service. You can truly only provide it on a one to one personalised basis. Its provision is part of your marketing. Its promotion isn't.