Actually a lot did. There were two strong migrations connected with the war industries in World War I and II.
According to modern liberals, they were living amongst a group of racist KKK type whites who hated them, oppressed them, and held them down.
Which is pretty much true. Blacks down South certainly were not loved, and the laws and social practices that were enacted to oppress them and keep them in their place were well documented. Things up North may have been marginally better in some respects but still wasn't welcoming. So if you're hated and oppressed where you are, why move 500 miles for more hatred and only marginally better treatment in other areas?
Either the oppression blacks faced down here has been overstated, or the tolerant attitude of the folks outside the South has been overstated, or both.
I would say the second point. The tolerant attitude of people up North towards blacks has been overstated.
If Connecticut or some other Yankee state had had a mass influx of blacks in 1902, to the point that they threatened to become the majority in the state, and to dominate politics, do you not think the officials there would have thrown every obstacle possible in their path? Poll taxes, literacy tests, grandfather clauses, zoning laws? Not to mention that they wouldnt have allowed that many to come in in the first place.
We'll never know.
Whites once had a racial consciousness equal to that of other races of people, but today they do not. Southern whites after the Civil War understood what would happen if blacks took power politically. Northerners did, too. That's why the Republican Party in the North largely didn't care that the South disenfranchised or segregated blacks after Reconstruction ended. Yankee Republicans would rather have the South run by Democrats, most of whom were pretty conservative, than to see the South turn into Haiti.
What they didn't predict was the rise of the welfare state, first under FDR, and later expanded in the Great Society years. Those events converted the black vote to the Democrats. That prompted Northern Democrats to suddenly wish to enfranchise blacks and to end segregation in Dixie, which in turn sent Southern whites into the GOP.
Today's massive centralized entitlement state thrives on "diversity", because the more "diverse" the population, the further the nation tracks leftward. That's why the Democrats don't want to control the borders. It's why the socialist parties in Europe want to import a zillion Muslims. Blacks, Mexicans, and Muslims have a strong racial pack mentality that whites no longer possess. Whites simply pack their bags and leave when things grow intolerable for them and their children, as they left Detroit and are leaving California. We have no NAACP or La Raza. We can't threaten to riot like the the Muslims did recently in Brussels.
What happened in the South after the Civil War is what happens when two races occupy the same territory and both races think in racial terms. What we see happening today all through the West is what happens when one race stops thinking in those terms, while the other races do not. Whites in Europe are "tolerant", the Muslims are not. Whites in the U.S. don't care what the racial make-up of California is, but Latinos do. And so on.