I wonder why no bank offers a debit-network-processed card that is backed by a line of credit.

Probably because there’s no money in it.

Fun fact: there are plenty of "credit card as a service" platforms nowadays so you could start one: https://www.getpliant.com/en/cards-as-a-service/

>debit-network-processed card that is backed by a line of credit.

Because then it wouldn't be a debit card? I assume that the debit-network is reserved for debit cards?

What would be the appeal of this to the customer? It is basically a prisoners dilemma. It is globally optimal to stop rewarding people for using credit cards but for each individual they lose if they don't do it. This is why in the EU regulation was passed to stop this nonsense.