Also, who says vim is running in a terminal?
I already use Tmux inside a tiling window manager and generally try to avoid manually managing panes inside Vim, mostly only tabs. There is a finite amount of hierarchical panes and tabs you can work with intuitively, before you wonder why they won't accept each others keyboard shortcuts, especially when you use the same color scheme in Vim, Tmux and Awesome.
> If I tmux then vim, I have to find some way to get the text out of tmux, and then back into vim.
That's actually a valid concern. I use piping for that, but it's not ideal at all. Maybe I will try it out.
Exactly the reason I want to manage terminals in vim. I already heavily use splitting in vim, and find it much faster and simpler to use than screen or tmux. In addition, I typically want integration between those splits, such as displaying the quickfix list in one, or showing 2-3 files in vimdiff, or yanking and pasting between files. Given that, I'd like to just open one more split in vim and have a terminal in it.
The original motivating use case for me: a vertical split, editing a manpage on one side, and showing a continuously updated render of the manpage on the other (using watch).