Honestly i doubt about part where the coin stay on hardware wallet since the website also say "Top-up & manage your card easily and securely through Ledger Live". Hopefully they don't mean you must send coin to card first so the card automatically convert the coin to fiat at time of purchase.
Both you and @suchmoon made a good point, haven't really thought about that part. In this case it's not any better than Binance as again your money will be controlled by someone else. And if I have to choose between two evils, Binance seems like a lesser one. Unless Ledger offers some crazy cashback amounts and additional perks.Of course, funding cards with crypto is only a temporary solution while shops don't accept crypto directly. Give it time 
That's how I see it and I think that people are impatient, and often forgetting how much was is done in a little bit more than a decade. Vast majority of those who think that it's a piece of cake for business to decide accepting crypto and that adoption is way too slow probably never owned any serious business and had that kind of responsibility. Talk is cheap. 4% cashback in XLM, and if you use USDC to fund it, since it's a 'stablecoin', there are no tax implications.
Are you paying those crazy high ethereum transaction fees for every transaction you make with your card?I think it's not so smart at all to use something like this when transaction fees can go over $100, and ''stable'' don't sound so stable anymore.