Thinking about gift cards in relation to ecash is pretty interesting.
If I ran a restaurant and sold gift cards and behind the scenes I used a Cashu mint to keep track of it, you might think it was not any better than the current standard of somebody's database.
If there were a lot of restaurants that did this, it still wouldn't be so different than the current situation either.
But if they pegged to bitcoin and had a gateway to lightning, all of a sudden you could use any gift card in the system anywhere that issued a gift card.
Okay, so there's a lit of problems with this: the main one being that it'd be really hard to make sure that the ecash was actually backed by what it claims it is backed by.
But here's the thing with that: when you get a Walmart or Carrefour gift card, you don't really worry about being able to redeem it, even though you haven't got a clue how many gift card liabilities they've sold and you surely don't imagine they are keeping the cash value of your card on hand.
This is probably because you don't have a huge amount of value there (nobody has a $10k gift card that I've ever heard of, but maybe I'm just poor). Also, these are huge companies, and so you kind of assume they'll be good for it, because if they aren't there would be some major signs. (For instance, when Bed Bath and Beyond was going bankrupt, I imagine people who had their gift cards redeemed them sooner than they otherwise might have).
I doubt we will ever get the interoperable gift card network of my dreams based on ecash, but I could see fedimints and cashu mints working like different sort of gift card, one that's much more transferrable.
Perhaps what you are buying when you trade btc for a particular mint's ecash is a functionality bonus (programmability) or a privacy bonus or cheaper cost of transacting. And when you peg out, you are selling those functionalities to someone else.
Last thought on this: why do people use gift cards anyway? I mean, if you are giving someone money, why nit just give them money? Why encumber it with restrictions? Is it just etiquette? Giving cash is an insult or paternal in a way that gift cards aren't. I think this plays a roll, but there's also discounts or perks merchants provide in return for money in advance. Maybe ecash mints will find a way to incorporate such things in order to attract users.