I would never even consider doing an unreinforced corbel, which is really the same thing. But I guess there's no reason it can't work in theory.
I flipped back to the image to see if there was anything clever happening where vertical load might put a vertical compression force into the key and effectively preload it against moment tension, but it's not in the right place for that.
Plain concrete theoretically gets used in foundations all the time, it just feels weird to use here. I did a quick flip through details and every other one I looked at has at least a bar on the one face.
Not necessarily wrong, but not what I would do.
But yeah, if you crack a section you have no tension capacity, so you can't treat it as though you're resisting moment by doing that. You either need to do plain concrete bending or just decide that you're fine with the load transmittal via inspection based on the ratio by treating it as near support shear or something.