Can't quote Air NZ, but I'm confident that both BA Holidays and AA have an approval mechanism. Even in normal times, when MMB's cancellation function was in place, payment had to be triggered by a human pressing "OK".

This doesn't mean that BA was right in removing the button, let me be clear. Personally, I like Ryanair's approach more: done 100% online but clearly saying that the refunds, if one wants them in cash, will be processed in 100 days or so. Not what one wants to hear, but at least it's clear and didn't require me to call 35 times for a voucher (and still I can't access the rebooked flights...).