Actually they do for MFA problems, even if you don't have paid support on your account. A few years ago I wiped my phone without first disabling MFA on my account (I use Google Authenticator). After business hours on a holiday, I submitted the support form [0] and got a call from a human five minutes later. He asked me several questions and deactivated MFA so I could log in.
Well, that's great, except, according to the article at the top of this thread, that's maybe not so great, depending on what kind of questions they asked you.
[0] https://portal.aws.amazon.com/gp/aws/html-forms-controller/c...