They treat it like the organization is attempting to commandeer someone else's account so all the privacy protections you expect for your own stuff is applied no matter how much you can prove it is not some other individuals account.
The best part is the billing issues that arise from that. In your example, if the previous engineer logged into that account (because they can) and racked up huge costs, assuming that account is getting billed or can be tied to your client, Amazon will demand your client pay for them, while at the same time refusing to assist in getting access to the account because it's someone else's. They hold you responsible, but unable to act in a responsible manner.
I know that that's not ideal, but as a practical matter perhaps it would be easier than creating a new account, if you can get the engineer to agree to it?
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.
In a past life, we printed the MFA QR code and the head of finance put it into a safe.