If filesystem access is a legitimate concern, you have bigger problems. Even if passwords were secured by FIDO or similar, session tokens are not. If you compromise a computer, you can compromise web sessions. There is no mitigation for this. Shame on the author for attempting to create panic when far more productive security can be achieved elsewhere.
- Sessions can be linked to a user's location and/or browser finger print
- Sessions are short(er) lived
- Sessions can easily get invalidated (e.g. device wide logout)
- Almost all critical actions are behind additional security (e.g. can't change password without 2FA or change billing information without confirming password and/or 2FA in order to apply changes, etc.)
- Sessions are not shared across properties, whereas many users share their password across multiple internet sites/properties