As far as I know, this generally doesn't work. A few years ago I attempted to cancel a gym membership, and after 15 minutes on hold on the phone I hung up and tried looking into banning a certain transaction or vendor from making another transaction. As best I could tell with my bank at the time (Bank of America), there is absolutely no mechanism to do this. The only similar thing they provide is contesting transactions, but that's only appropriate in the event of fraudulent transactions (which a recurring gym membership arguably is not).
I was able to get out of a similar situation by threatening to contest the transaction. Basically told them “alright, have fun duking it out with my credit card company” and they immediately backed down.
I'm not sure how it works with all processors, but at least many of the ones I'm familiar with have a flat fee that's assessed for each chargeback. Stripe, for example, charges a $15 dispute fee (https://stripe.com/docs/disputes). For many companies, incurring disputes is something to be avoided, and threat of one is enough to warrant bypassing many normal process that exist to stop cancellations / keep people committed.
