We should not miss the point that slaves were not allowed to vote but the south wanted them counted to increase representation and in essence, vote as their proxies. The opposing view was since they can’t vote, they can’t be counted.
The whole idea of “personhood” is nonsensical when the south considered them non-persons and the north said basically, if that is your view, non-persons can’t be represented.
It was a classic compromise where neither side got all of what it wanted, but yielded since the formation and survival of a nation was at stake.
Ironically, it was one of the least debated parts of the Constitution. "We want this." "We want that." "How about 3/5?" " Okay." "Next item?"