None of this will get kids taken by CPS in any state (if they follow the rules on the books, that is). CPS is taught to respect family culture, and they *do* allow corporal punishment that doesn't leave marks, and all the rest of the things you mention. Absolutely none of that - spanking, occasional bed-without-supper, grounding, homeschooling, one-room-schooling, non-vaccination, midwives, abstention from federal documentation, lack of electicity/computers/cars/photos - is illegal. (Meal punishments can typically include "go to bed without dinner" once in a blue moon, but not missing meals with any kind of frequency that would leave a child regularly hungry or malnourished.)
To be very clear: what you listed that the Amish do (assuming it meets the guidelines I mentioned above) is not illegal. It is not considered child abuse by the law or by CPS, regardless of what you or I might think.
What the Harts did - closed-fist beating over a bath tub that left bruising from sternum to navel, dunking head under cold water, withholding meals regularly and/or for days - this is not legal. It's abuse and neglect.