Here's an interesting experience, though.
In advance of our move to the US, I rang one of my credit card providers to cancel my card. Both Wonderful Husband and I try to pay off our credit card balances at the end of the month. In the process of canceling, I was told that because of my 'excellent' track record, they were prepared to lower the interest rate on the card by about 4 percentage points. (From about 15.5% to 11.5%)
Although that's not terribly meaningful if you pay off your balance at the end of the month, there are times when we use a credit card to take two or three months to pay for larger items.
Like many people, I've tended to leave my financial arrangements in place rather than asking for a better deal. And, apparently, at least one company is prepared to try to offer a deal if they want to keep your custom. It's the principle of 'If you don't ask, you don't get.'