They weren't fighting for the "Constitution"; they were fighting so a few jerks could keep owning other people.
And not even because the end of slavery was imminent. It would have still taken decades for enough legislators to be elected to outlaw it.
Wow, now you are just making things up, aren't you? Hundreds of thousands? Really? Even Axis Mikey wouldn't try to peddle bullshit like that.
You kind of stumble into a reality, that the North won the War and lost the peace. Grant did send troops in to eliminate the KKK, but presidents after him (shamefully) allowed Jim Crow, sharecropping, and debt peonage to re-establish a racial hierarchy that unfortunately endures to this very day.
So the North didn't really want to enforce civil rights, and the South wanted to pretend the Civil War was a great "lost cause" that was about issues other than slavery.
Kind of like when a white trash father goes on a drunken rampage, but the next day, everyone pretends it didn't happen.