You have a strange idea of what caning entails. It's literally just x number of solid smacks on the behind by a trained administrator with a wooden rod. It's not a random beating a la Dwarven Justice. Singapore even puts padding everywhere else on you in case the dude misses, and a doctor is required to be on-site during and afterward to treat any bleeding.
no, i've just been taking folks at their word on the assumption that caning is just an example of a more extensive system that incorporates corporal punishment
at some point such a system is all but certainly going to include a more severe sort of punishment to handle cases where a beating light enough to have no long-lasting effects is just not going to be a deterrent
you're faced with a catch-22 of sorts - either the violence is inadequate to deter any but the most petty crimes, or it's provided in conjunction with other punishments, or it's so violent that it requires a meaningful recuperation period
and the middle option, while probably the best, raises the question of why you're not just using the other punishments, a la the plan to supplement human batteries with some kind of fusion technology
and good luck convincing the sorts of folk who
want corporal punishment that they should pay for any medical consequences that arise - the "let's deter crime with violence" crowd does not overlap strongly with the "let's reform criminals even if it means being nice to them" crowd, although i guess the fact that we're even having this conversation makes it a nonzero overlap