You can do the same thing in the US. The problem is that businesses can't easily do this without collecting bank routing information from customers, which is effectively "secret" because it allows anyone to debit money directly from their bank account, so they're reluctant to provide it.
What's needed is a low- or no-fee system for requesting payments from someone without collecting any secrets from them. The technology to do this is not hard -- use public key cryptography, or just require the customer to approve merchants before they can make debits. But the customer's bank has little incentive to implement this because the customer won't choose a different bank over it and meanwhile the banks own the credit processing networks charging the high fees.
Which is why people are looking for an external solution.
How does it work in the US?
But with the same information someone can also make a withdrawal, which is problematic.
You seem to be talking about authorising businesses to take money from my account without needing further approval. A direct debit.
Parent is talking about transferring money to someone else's account, which is easy and requires no secrets or authorisation.
What problem needs to be solved?
This would be essentially solved with a standardized system for customers to give each merchant a separate bank account number (or equivalent) which really refers to the same bank account but could be revoked individually if that number is compromised or you want to remove the merchant's access, or could be set to automatically expire for non-recurring payments. But the banks don't have the incentive to provide this when they're the ones getting the credit card fees.
Supposedly FedNow is the solution to this, but it will be a while before this functionality is exposed to end users.