Surely you know that the lineage goes further back to the Mozilla Application Suite and then Netscape before that?
Right-click each folder, properties and check "Check this folder for new messages". Or set the global 'mail.server.default.check_all_folders_for_new' config to true.
I don't understand why that isn't the default.
> Maybe they should dedicate some s/w effort to making it actually fetch mail into folders BEFORE you click on them
Click right on folder, options, enable "always sync this folder when getting mails for this account'