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Which country/processor? This is normally regulated and there are explicit processes around chargebacks. It's surprising/suspicious that you'd ever be refused one.

Switzerland, UBS card.

Chargebacks happen after the fact; they won't prevent the same merchant from charging you again in the future. (You can, of course, issue a chargeback on those payments as well)

Your card issuer (at least in the UK) is obligated to block recurring payments from a particular merchant if you request it

https://www.fca.org.uk/news/news-stories/continuous-payment-...

It's a credit card thing (which arguably are much more common in the US).

Getting a new card doesn't necessarily stop recurring bills as trusted merchants can use features like Visa Account Updater or Mastercard Automatic Billing Updater. Though in practice, these trusted merchants usually have easy cancellation flows.