The 14th amendment was cleverly designed to try to force the Southern states to let black men vote, without also forcing Northern states to do so (some at that time still restricted voting rights to white males). The threat of reducing representation in Congress was meaningful when applied to Southern states where a sizable portion of the population was black, but at that time Northern states had black populations which were 1% or less of the total, so they would not be penalized.
In practice the threat of reducing representation was never carried out, and the 15th amendment in 1870 extended voting rights to black men in all the states. (The Republicans had realized that even though there were not very many black men in Northern states, their votes might make the difference in a close election--and they would all be voting Republican.)