The common misconception that swap is pointless stems from misunderstanding what it’s supposed to do. You shouldn’t be triggering the OOM killer frequently anyway. In the much more normal case where you’re only using some of your RAM for running applications, the rest is used as a filesystem cache/buffer. Having swap space available gives your OP the option to evict stale application memory from RAM rather than the filesystem cache when that would be the optimal choice to make.
This page explains it detail: https://chrisdown.name/2018/01/02/in-defence-of-swap.html
Nobody can have proof of that, because no such proof can ever exist. How would you ever have a proven correct number of cheaters not detected?