Good example for Mersenne Twister and naive parallel random number generation in R failing

It is often discouraged to generate random numbers in parallel calculation in R by simply setting sequential seeds for each parallel process like

library(parallel)
cl <- makeCluster(4)
y <- parLapply(cl, 1:10, function(i) {
  set.seed(i)
  runif(n = 5)
})
stopCluster(cl)

(code from https://www.jottr.org/2020/09/22/push-for-statistical-sound-rng/).

I could not find any example that would reproducibly demonstrate a problem with this 'naive' approach.

How can I demonstrate the potential issues with this naive approach?