I would like a little better explanation of how "decentralized debit-cards" are supposed to work.

Are they supposed to be able to be used at point of sale purchases? If so, how is that supposed to work? The reason businesses except your current banks Visa, or Mastercard debit-card is because of the centralized entity(Visa, or Mastercard) that backs up the purchases. Anyone could print up a bunch of cards that are not backed by Visa, or Mastercard....but no one is going to accept them for purchases.

Banks also offer a non-branded debit-card for people with only a savings account. This debit-card is only used to withdraw money from your banks ATM. It cannot be used for purchases. I do not see how this could be an option either because you need the centralized entity(your bank) to hold an account and offer withdrawal services through the ATM.

None of the above would allow even a fraction of decentralization.