They aren't allowed to charge you whenever they please, without customer control, they have to abide by the contract. Unfortunately, most people don't read the contract, and companies put ridiculous terms in there that people happily agree to.
I propose the following: a ToS is accompanied by an audio transcription playing at average speaking speed. A person can only use the service after the whole thing plays. We'd quickly see a race for short ToS.
Or maybe require layers to accept ToS. If lawyers wrote them, maybe it would be helpful for a lawyer to read them to consumers! They could even amend it and negotiate changes with the service provider - maybe the terms are not compatible with their client's Terms of Consuming.
These are just joke scenarios, but they show the power imbalance between service and consumer.
A customer will be well within the bounds of the contract if they cancel their mandate through the bank, as long as they also don't expect to have continued access to Netflix.
Even in the US, there is nothing stopping the customer from closing their credit card account, except that it is an unreasonably inconvenient for the customer. It is far simpler and IMO sensible to be able to revoke consent for specific purposes through my payment instrument. So why doesn't the banking system in the US provide this as an universal option to customers? After all, this is exactly what Apple facilitates albeit at a high cost.
You can ask a US bank to stop future payments to a given merchant, but it doesn't actually absolve you of your contractual agreement to pay the merchant. Most internet based services have decided that it is bad business to pursue accounts where the payment was unsuccessful, but from a legal perspective, you are still on the hook.
I'm not saying I agree with the way the US system handles this, but to say that "the norm in the US to allow companies to charge their customers whenever they please, without the customers having any control" is inaccurate since customers have agreed to the terms of the contract which define when the customer is charged and what control they have.
Unfortunately, we lack laws to mandate easy-to-understand terms of service that highlight the most important information in a way that actually serves the people instead of businesses.