You can use one for most of these functions if you switch to a tiling wm. i3 is popular and has very good defaults I find, I don't really need tmux when I can arrange terminal windows however I like with it.

Most tiling WM's are essentially 'tree style tabs' but for all windows. You organize tiles and children of a tree, in i3 you can also set tiles to stack so you get a tab-like appearance to a tree.