Not disagreeing with this (although my understanding is that there have been studies that show vaccination has been more effective), but how would you seperate the unvaccinated / previously-infected-and-recovered cohorts?

Even by reconciling PCR testing data (which I imagine is incredibly patchy at best), you still would only know historically how many people tested positive (ignoring what is in all likelihood a majority of the cases that never got tested) and be able to reconcile it against numbers of vaccinated, which tells you nothing useful without being able to intersect the two sets (which you can’t do without uniquely identifying every PCR test and matching it to an individual universally).

i.e. the better data you would need doesn’t exist.