I think the era the Jim Crow were passed was critical. The mass voter suppression didn't actually start showing itself until the late 19th century. For instance, I'm just going to take one state (perhaps the most corrupt state), South Carolina:
1870 Census: 705,606
1872 Election: 95,452 total votes
1880 Census: 995,577
1880 Election: 169,793 total votes
1890 Census: 1,151,149
1892 Election: 70,504 total votes
1900 Census: 1,340,316
1900 Election: 50,812 total votes
1910 Census: 1,515,400
1912 Election: 50,405 total votes
1920 Census: 1,683,724
1920 Election: 66,808 total votes
1930 Census: 1,738,765
1932 Election: 104,407 total votes
1940 Census: 1,899,804
1940 Election: 99,832 total votes
I made a
thread about census population history, if you want to see that as well. So yeah, the laws definitely didn't go into affect until well after reconstruction. The laws not only made voting harder, but made voter registration harder. I can imagine many white people, especially poor white people, just said forget it, and they didn't vote. And black people probably were subject to violence if they tried to vote in that time.