Out of curiosity, in Canada (and the USA, where I assume it will be similar), how do you call the system to authorise a business, for example a utility company, to charge your bank account directly every given period, with a more-or-less flexible amount, and with no need for you to take any action?

The reason I ask is that that is what is called a "Direct Debit" in the UK and the European SEPA area, and it does not involve providing any credentials to the bank account. Rather, you only need to provide your International Bank Account Number (IBAN) and maybe your name. However, the ability for a company to be able to take Direct Debit payments is heavily regulated, you can easily cancel them via your bank, and even reverse charges if they were illegitimate.

This is as common as bread and butter in Australia. You provide your bank account (or credit/debit card) details to the company or even govt (gas, electricity, water, car registration, insurance, internet, mobile etc.) and a so called direct debit authority and the company will just debit from your account on the due date.

Yes, Direct Debits or similar are something that I would normally assume is commonplace in every developed country. However, I'm so aware of the American TV trope of receiving "bills" in the mail and having to remember to pay them that I wonder if it's just something that has stuck as a cliché even if it's no longer the case, or whether it is still the ordinary way of handling these payments in North America.

Yeah, direct debit is a very specific, well-standardised thing in the UK and comes with a fair amount of consumer protection. It’s also a bit Oauth-ish in that you can unilaterally cancel it from your bank’s side of things instead of going through the provider.