So you can add a new file to a channel but not to a chat. Unless I'm missing something you have to create a file locally and then upload to a chat. It would be nice to add a file within a chat just like you can do within a channel. Or maybe that's on purpose?
I think it's on purpose because in order for the file to be shared some custom code would have to go into the office web apps to share it after clicking new etc since files are stored in your OneDrive then shared out with the recipients in the chat.
With the new button on a Team, a file is just created and permissions do not have to be touched. Therefore making it easier to just create a file than to mess with permissions and sharing like a chat would have to do.