The whole "I'm afraid that won't be possible" used socially in terms of etiquette is a different beast. There, it is usually an individual making decisions for what they personally will or will not do for someone.
Businesses use it to put off customers, no doubt. But, it doesn't mean that the customer is being rude to ask for a supervisor or ask to go up the chain of command.
I agree with your whole post, and in particular with the portion I've quoted here. "That won't be possible" in a social sense is quite different from the same sentence in a business sense.
Where I work, we sell punch cards as a way to pay for our services (one punch per visit, 10 or 20 punches per card). It's one of several ways to pay for our services. Our punch cards are listed as "non-refundable", and part of the reason for that is that we don't want to be on the hook if someone loses their card. I'd guess companies that sell gift certificates have the "no refunds" policy for similar reasons.
However, as the supervisor of my department, if someone presented what seemed a valid reason for wanting a refund (services not provided as expected, dissatisfaction with an employee, injury preventing them from using our services), I could
offer them a refund. If the reason involved dissatisfaction with services provided, I'd address that first and try to get the customer to give us a chance to make it right, but ultimately I can
refund even the "non-refundable" card. (I will not, however, give any exceptions to this policy for a lost card - keeping track of your card is your own responsibility.)
I have, in five years, refunded a punch card only once. And I did expect the customer to give me the punch card back when I refunded her, to avoid her using it even after receiving her money back.