With a vaccine, you get a standardised dosis of an agent resembling the disease or just a part of it. The remaining variability is the response to that standardised input.

With an infection, you have no control over the degree of exposure, so on top of the variability of the response comes the variability of the exposure.

Additionally, in case of exposure of the full pathogen, there is some variability to what part of the pathogen the immune system will respond. That part can actually be a good thing in total.

Nobody knows what dose was delivered to the “natural immunity” group, how many times, or when.

there are very similar issues with the vaccine - the same dosage of the vaccine will not behave the same in everyone

but this is a good point I hadn't considered, thanks

Seems we should be able to test for antibodies though. Why aren't we?

we are testing for antibodies but antibodies aren't the only immune system response and depending on who you ask might not even be the "main" defense against covid.

It's a blood test, and I suspect that it's even harder to motivate everyone to get a blood draw than to get a vaccine.