> it won't (logistically can't) work when you have literally run out.

While I believe you're correct for the iPhone, that it won't work, it's actually not as impossible as you suggest. The NFC-capable BlackBerrys that supported the very early tap-to-pay with a phone had the concept of a default card, which could be programmed onto the secure element and would work even if the phone was totally dead (even if the battery was removed). The NFC field was enough power to boot up the secure element, just like it's enough power to run the chip in your bank card when you tap it.

Later phones dropped this support, as it took a bunch of engineering effort and customers largely didn't care. But if customers ever start demanding it, so they can totally stop carrying a bank/credit card, it is possible.