What exactly is the point of giving me SSH/sFTP access but not giving me the ability to change the permissions?
I'm in FileZilla, trying to delete things, overwrite things, etc, and I can't because the permissions don't allow write. And trying to change the permissions within FileZilla doesn't work.
I haven't had this issue before, what changed?
This could be a FileZilla or GoDaddy issue.
Got two solutions for you.
FileZilla, they did recently come out with a new update and change the way things appear. Try right clicking on the file you want to change permissions of. There should be a menu that says 'change permissions' after right clicking.
GoDaddy, try creating another ftp account and be sure to grant the new account permissions to do everything.
I talked to support. They just don't give managed WP accounts write access. Super lame. Not much use in having FTP access if you don't have write access.
Why you don't have write access to folders outside of plugins, themes and uploads?
Because it is wordpress hosting. If you change other files it is no more wordpress. But you could download and save the other folders and files for local testing.