While this article was good, it omitted one very important check: that of keeping cabinets in plane to each other. It is possible to have cabinets level, plumb, and square as you recommend and still be out of plane.
Imagine a kitchen wall that starts to go out of plane at the left side of a freestanding-range opening. If the cabinets follow the wall, the right cabinet will be farther back than the left, and the cabinet installer has left the countertop installer with some unpleasant choices. If the countertop man keeps the depth of the tops on each side...
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