Similar to my idea but he's using 2 belts which will up the cost plus the extra bearings used.
Also makes mention of reducing backlash etc.
Just had a thought against my idea lack of actual drive as only one tooth would be in contact.
Back to drawing board!

You can use one belt but it still needs to wrapped around the pulley, this causes probems with backlash due to the belt stretching and sagging. (and between belt and pulley)

In the other design two belts (or 1 cut in half ) are required to solve this and increase the tooth count on the pulley. The bottom belt is fixed and acts as a rack. the top belt is used for driving and the bearings force the top belt back down to mesh with the lower one forming a solid. Belt stretch is greatly reduced as it is only the small portion over the pulley and the sagging is removed. one thing to watch is that the belt can take back bending.

As you pointed out this all added up and I have mainly seen it used on on large machines where ball screws would need to be massive. you could compromise and just provide support for the belt to remove the sagging.