There's a lot of evidence that once a punishment is big enough, it makes no difference on deterence, but that's very different from saying punishment vs no punishment is the same.
https://www.publicsafety.gc.ca/cnt/rsrcs/pblctns/ffct-prsn/i...
https://nij.ojp.gov/topics/articles/five-things-about-deterr...
There's a lot of evidence that once a punishment is big enough, it makes no difference on deterence, but that's very different from saying punishment vs no punishment is the same.