I strongly agree with the rest of your characterization of the AWS console, but that one isn't true: https://docs.aws.amazon.com/IAM/latest/UserGuide/id_roles_us... -- we use IAM Roles extensively at $DAYJOB and have not yet experienced anything that would require a Chrome extension to work around like you describe
Their login screen, however, continues to drive everyone crazy since the URL you visit depends greatly on which account, and at what level, you wish to authenticate to the console. With any setup containing a non-trivial number of AWS accounts, it's just "oh, what account am I logged into" waiting to happen