Because corporal punishment is an ancient display of power; the master holding the whip and the servant being punished for misbehavior. It's obviously effective, and undoubtedly more humane than incarceration, but it's also anathema to the morality of the "free society" where everyone is supposed to be equal and thus no-one can hold the whip.

(Heck, even disciplining a child is considered grounds to put the kid in foster care; if you want corporal punishment v incarceration, that's a hell of a dichotomy. And for every genuinely abused kid CPS saves, how many healthy families get broken up again?)

The idea is childish and unrealistic, but nonetheless popular because it plays on the fear and resentment people feel towards those above them. And in a democracy, popular sentiment is difficult to defeat.