I understand your logic, but here is the way I would think of it.

$800 for the 17-55, $1000 for the 7d gives you $1800 US. $2,049 buys the 24-70mm II at B&H. You will need $240 +/- This gives you Canons best higher MP camera with Canons best in class Zoom.

What you give up is a backup and a OK BIF set up, but not a great BIF setup.