Know any companies that reward loyalty?

Just helped my mum renew her household and contents insurance. Her and Dad were with the same local broker for thirty years and are the sort of people to whom it would never occur to make a claim, even if their house fell about their heads!
This renewal, I did a momentary online search and found dozens of cheaper policies, with all the same benefits. I phoned them to say I wouldn't be renewing, as I didn't want them calling mum and confusing her. Their response to my telling them I had found a cheaper quote was to ask if we would stay with them if they matched it.
My reply
"Duh!!! No!!!!! If after all these years you are not giving us the BEST service straight up - forget it. I wonder how much Mum and Dad have overpaid over the years by trusting that broker.

Yes - good response Chutzpah! - I must store the suggestion that they improve on, rather than just match, in my repertoire! Why don't they offer better rather than match? Anyone out there work in that sort of situation and can tell us what flexibility is allowed?