The compromise limited the disproportionate influence the slave states had in Congress but it did not eliminate it.
Had the South dominated as you inferred, then slavery would have spread to all other states, and slavery as an issue in the Civil War would never have happened.
The Northwest Ordinance, Missouri Compromise, and Compromise of 1850 had more to do with restricting the spread of slavery to the territories than the 3/5ths compromise did.
The compromise limited the disproportionate influence the slave states had in Congress but it did not eliminate it.
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It was a compromise! Not supposed to limit it, but to keep it from immediate take over and expanding to future states and territories!
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The Northwest Ordinance, Missouri Compromise, and Compromise of 1850 had more to do with restricting the spread of slavery to the territories than the 3/5ths compromise did.
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The later laws were LATER and where certainly influenced by the original 3/5ths ... The Northwest Ordinance 1789, The Missouri Compromise 1820, The Compromise of 1850