That got done recently for transmissibility recently with the Danish study (which finds no difference in intrinsic transmissibility between Omicron and Delta and that the advantage Omicron has is entirely immune escape):
https://www.medrxiv.org/content/10.1101/2021.12.27.21268278v...
Then your unvaccinated group that you're comparing to in the Delta and Omicron waves are equally susceptible to disease and any cryptic spread and immunity may be present but will be equal.
The South Africa study cannot do this which means they're comparing different time points and they have many confounding factors. That is not strong evidence.
Plus best they get is that Omicron is about 1/4 of Delta which is 1/2 of D614G which is still terrible. That is still just SARS-CoV-2 levels and not the factor of 10 that would turn it into influenza.
That is likely due to so many people being vaccinated or recovered.
If you dropped Omicron on the world population in the middle of 2019 I strongly doubt it would be any more mild.
> A lot of the deaths occurring right now are still from patients that were infected by the Delta variant weeks ago.
I guess natural immunity isn't as consistent as vaccination though (which produces exactly zero shock amongst the world's virologists and epidemiologists) and also suggests that Omicron isn't intrinsically mild at all.