Closing your card doesn't have any impact on legal obligations you had, or a merchant thinks you had, or any impact on whether a merchant will choose to do business with you in the future.
In terms of merchant choosing to do business with you in the future, they may or may not have a choice; depends what they use to identify you with. Certainly, if they don't make canceling easy, it's probably not the kind of business you want to deal with.
All that said, this is why anything that auto-renews, that I don't know if I want to keep renewing (i.e., will I still be using it at the end of the trial period, end of the month, end of the year), I immediately cancel. If it's a trial and that terminates access, I will take that as a sign not to use them. If it's paid and that terminates access, I will also take that as a sign not to use them, but I'll also email them and basically say "hey; I paid for X period, wish to use it for X period, but am unable to use the service for X period. I either need you to reinstate my account, sans auto-renewal, or I expect a refund". That tends to get a response, since otherwise -they- are legally on the hook.
Near it the price information carries the monthly price only, with no indication that you are signing up to 12 times that amount.
The only saving feature is that you don't need to read dozens of pages. If you open the contract, it is confusing from page 1. But it's also not clear at all what is going there.
This will invariably lead to a terminated account and a bunch of declined emails , but thats as far as it goes.