The money is taken from the credit card company, then. The architecture is still pull. You're splitting hairs.

That's not splitting hairs; that's literally the point of credit cards. It is entirely "push" from my perspective, modulo the minimum monthly payment and tolerance for paying interest and bad credit.

If I buy something with a credit card for $2k and have $2k in my bank account, the $2k is still there until I pay the credit card company. It could take years or be paid off immediately.

It's not a "pull" at all.

It is a pull. You bear the costs of fraud whether you notice them or not. The fact that the credit card company hides those costs from you doesn't change the fact that their architecture is broken, and that you are still paying for it by virtue of the fees they charge merchants, which create higher sticker prices for you. Costs like that don't simply disappear into the ether - you, the consumer, pays them.

Every consumer who doesn't use credit cards also bears the fees since it is rare to find a merchant that offers a "cash discount".

Ya, also true, and good point.

Precisely none of that is "Every time you use your credit card, the store takes money from you."

It's a pull architecture. Pull architecture is wrong, push architecture is right.