This 20+ years ago, I think look up "guan" / 管 (to govern) parenting style studies. For quick search, maybe research by Shek on HK school kids, only because name sounds familiar, I don't have access to psych journals anymore.
https://pubmed.ncbi.nlm.nih.gov/18047239/
I think look for east asian studies on behavior control / psychologic control and academic outcomes. Usually it was framed in kids raised by "invested" parents with (or without) CP will do better academically than kids who are neglected, i.e. hands off parents. Caveat those research shows CP can still lead to emotional regulation problems, but also higher academic achievement, which IMO what literature / or western rational misses, it's very east asian lens though, you raise kids do well in school, they will get decent opportunities in competitive east Asian environment -> integrate better with society -> have less chance of antisocial behavior.
Rest personal opinion.
I think studies even then say CP also reinforces entire generational violence cycle etc, shit west find horrid, but in east asia it just means strict parenting with optional CP -> prevent anti social behavior... so generation CP loop not virtuous or anything but functional. Like from memory the studies were not pro CP, or CP doesn't have negative effects, just CP effective corrective tool for some, which when applied to east asia society/social layer = if your kid going to have no future without CP, might as well as apply it, because beating a kid to pass national exams opens more opportunities for good life than not. Kids there have that context for "tough love". Asia diaspora with academic focus brings this with them to west. Same from other diaspora (i.e. first gen immigrants from poor countries) that beats kids for not trying hard enough to "make it" because they're socially disadvantaged vs locals/natives. Then subsequent generations adopt western soft parenting, grades / work ethic reverts to mean, which IS (generally) fine in advanced economy context since you can be pretty stupid in west and still do alright. Hence in west-minded find CP archaic, until west starts realizing soft parenting is generating soft populous that is geopolitically not competitive (current anxieties)... which was previously covered up via immigration... from diasporas that are not soft.
Singapore executes like 20 people a year, there are way more than 20 bad apples there. Either way, I think punitive state violence and corporal punishment as parenting instrument different topics. Should state beat people for deterrence, I don't know. Does it have affect on social order? I think statistically likely, maybe not worthwhile. And for some cultures mass catharsis from punitive justice is not... unuseful. Does it prevent individual recidivism? Broadly I don't think so, desperate people do desperate things. Should parents have CP as tool? Yes, shouldn't be universal but also not prohibited - some kids might need a slap or two early in life to shape behavior that correlate with social / upward mobility "success". Which matters in some society much more than others.