Can we expand on that?
Would we have less black crime and particularly less black on white crime had Jim Crow been maintained and expanded?
Possibly. Just as we might, possibly, have a more orderly society if the aristocrats of the early modern period and the Catholic Church had maintained their monopoly of power.
Of course, keeping Jim Crow would have been at the continued cost of ignoring the principles we supposedly stand for. If being an American conservative means fighting for the principles embodied in the Declaration and the Constitution, then opposing Jim Crow is an eminently conservative position.