373-5(c) requires that "cables shall be secured to the cabinet..."
There is an exception for surface mounted cabinets, but there are 7 items that must be complied with to do it right.
As far as the max size cable is concerned, you have 1 inch in the center of a 2x4 to use without needing nail protection, see 300-4(a). You might, if you hold your mouth just right, get #2 aluminum SER cable to go through a 1" hole. I certainly wouldn't want to run this size cable through too many holes, my back hurts just thinking about it.