An easy way to quit.
When you sign up for $Service use a Pay-As-You-Go (PAYG) refillable credit card like the kind you can buy as a present for someone, deposit a few $Currency into, then send as a birthday gift. The recipient of the PAYG card can use it as any other credit card, but only up to the balance currently on the card. You can't become overdrawn on it, it auto-stops allowing use the moment the balance reaches 0. You have to top it off before you can use it again.
By using a PAYG card as the default payment instrument for $Service, that service will have a quick, dirty, easy, & fulfilling means of quitting their clutches -- just don't top off the card. Let it expire with a 0 balance. The next time they go to charge you for something, they hit a brick wall of "Insufficient Funds: Charge Denied". They can complain all they want, you don't have to refill that card until whatever issue started the whole mess gets resolved to your satisfaction. And since a PAYG card does NOT require your Personally Identifiable Information (PII), there's no need for $Service to even have your real PII either.
I signed up to Amazon with a PAYG card & using an Amazon-specific pseudonym. When they tried to screw me over & charge me three times for stuff I hadn't ordered, I stopped refilling the card & told Amazon to kill the account. They refused & demanded payment. I told them to get stuffed. The only semi-real PII they have on me is my email address, and THAT includes the Amazon-specific alias to let me know where it was used. (I've mentioned this tactic before.) They refused to kill the account, so I logged back in, scrambled all my already-fake-PII, saved all the changes, & religated the Amazon-branded-email-alias to the junk folder.
Any time I get email from Amazon, or a statement from the PAYG company reminding me to refill the card "to restore functionality", I laugh & give Amazon TheFinger. They want to screw me over, I don't think so, and so Amazon gets to suck eggs.
TL;DR: The quickest, easiest way to quit a service that wants a credit card is to use a PayAsYouGo refillable card that can be safely tossed in the trash bin when said service turns out to be social underwear skidmarks.