That's not an equivalent analogy. A better analogy would be to say I had a bank account and I told my bank to call up Joe on the phone when confirmations were needed. I still have the account, but I have fallen out with Joe. I want the bank to call somebody else, but they refused to do so, even though it's my account and I'm paying the bill for it!

Banks have established processes for changing signatories on business bank accounts, including in situations where a past signatory is no longer with the business.

In a nutshell: if a past signatory was a regular employee, it just takes any other signatory to remove them. If there was no other signatory, or if the past signatory was an officer, it takes a current officer (as set forth in the company's AOI or corporate minutes). Usually only the latter 2 situations of the 3 above require an in-person visit to the local branch office, and that only requires a few minutes.