> Since initial infectious doses and peak viral loads seem to vary wildly in people who've been infected, I would speculate that it's much easier to quantify vaccine-induced immunity in a public health context relative to so-called "natural immunity", since those initial variables can be tightly controlled.
I think you are missing the largest discriminator.
The US Vaccines[1], and the related vaccines, are highly limited resistance specific to a spike protein only, perhaps with boosters, to a number of spikes seen. Total = 1, perhaps 2 if it includes a delta variant spike booster also.
Natural immunity confers with it resistance to a number of different covid-19 viral proteins, not just the spike. We know Covid-19 has 29 proteins
Now, we know that researchers saw these antibodies, as they were the ones that said, "all these antibodies could be the target of future vaccines", and the idea is there. However, we don't know the exactly count of antibodies to all these viral proteins, we just know of their existence from research. [2]
But, to compare the strength of natural immunity to a vaccine is to fail at elementary math.
However, I am not saying that people at a high risk from age, comorbidities, or both, should not take the vaccine. That is their own decision. On the other hand, the vast majority of the research indicates that natural immunity actually provides superior immunity from a breadth perspective, since a legacy vaccine protection is comparatively challenged against a mutated spike.
[1] This is not true for all vaccines, merely "spike" vaccines. So, it wouldn't apply to an attenuated viral vaccine. However, attenuated vaccines do not prompt as strong an immune response.
[2] https://pubmed.ncbi.nlm.nih.gov/32555388/