You can read about how it works in Singapore at the Wikipedia article:
https://en.wikipedia.org/wiki/Caning_in_Singapore
The description of scarring and motion difficulties for up to a month afterwards are more severe than I'd expected. The lashes are not delivered in public.
There are some ways in which Singapore is "the western world", by language/culture/legal-system, though not geography. As the article notes, their practice of caning was inherited from the British.
I share some of the visceral discomfort with the idea, but also know lots of things we allow because they work, or are within someone else's preferences, also cause many people visceral discomfort: organ (or fecal!) transplants; non-majority sexual practices; legalization of drugs or prostitution (some western world jurisdictions). Disgust is often a hint, but not reliably dispositive, about what should be allowable.
We also allow solitary confinement and the death penalty, despite evidence these have weak deterrent effects, sometimes causing grave psychological damage or the death of innocents. What if we studied the matter, and found evidence that corporal punishment of adults better deterred crime, with less follow-own damage, than these traditional practices. We should probably then ban those familiar barbarisms, but still consider as possible the far milder action – lashes – that seems like a barbarism from unfamiliarity and gut reactions.