(Click to enlarge)

We currently do this on mobile mode for the frontend theme (not the admin theme I think), a responsive one would do this based on viewport size.

I probably should have clarified... using a vertical menu on the left side of the screen... not the kind of vertical menus Composr uses now (where it takes up the entire width of the screen and displays at the top rather than the side).

I've never seen Composr use a left-side vertical menu before.

I still need convincing on this. The 'selling points' seems to be to reduce scrolling for tablet users, but said tablet users aren't going to have large enough screens anyway unless in landscape mode, which most users won't be.

To be very honest, I haven't a clue on the technicalities behind this style. A lot of systems use the left side menu for when the screen is wide enough because it looks attractive and makes the menu less obtrusive. But as you said, the screen needs to be wide enough or the side menu will cram things.

Right, on that basis it's probably best to leave things as-is, because page weight is also a concern.