Chargebacks are a thing, but they require constant vigilance and the occasional bureaucratic task.

Everyone already has the basic ability to pull funds from arbitrary checking accounts. heh.

This simply isn't a thing in the US, as I discovered when moving to there for a time. They use third-party apps, cheques, and wire transfers (which are expensive and seem to work via ACH, a pull type system). It's simply not possible to go into your ebanking app and transfer money to someone elses account. (With very restrictive exceptions, e.g. same bank, or maybe the bank has integrated a third party service...)

As inconceivable as the American system is in the beginning for somebody coming from the EU, I guess for many people from the US it's similarly non-obvious that a push system can (and does) exist somewhere else.

which has your account information on it

(I do the same thing, though.)