Except protection from natural immunity is weaker than the vaccines and more susceptible to variants, thus significantly increasing the likelihood of reinfection and passing to others. I can appreciate the debate, perhaps a test to show natural immunity would be sufficient, but there's certainly a case to be made beyond "pure theater."
>Natural immunity is ... more susceptible to variants
Do you have a source for this? I have looked it up a few times and all the information I saw indicated that natural immunity should transfer to variants favorably, because natural immunity targets several parts of the virus whereas the current vaccine only targets a single region.
>natural immunity is weaker
This is true on the margin, but it is still quite good. Vaccination breakthrough cases are very rare at <0.1% of cases[1]. The CDC reports that natural immunity breakthrough risk is 2.34 times higher than vaccination[2], but you have to remember that the base multiplier is still incredibly low. By this logic, cases from natural immunity are at worst 0.23% of all cases!
I think it is very misleading to be grouping those with natural immunity with the unvaccinated when it is so close to vaccination in efficacy, and drastically different than those with no immunity.
There's no scientific evidence anyone has a "natural immunity" to SARS-CoV-2, and even the immunity granted to those who are vaccinated is largely contested by the mutations known as the delta and lambda variants.
The situation is not that obvious, and thus different places evaluate it differently. (E.g. here in Germany the protocol is one vaccine dose a few months after the infection, based on results that this has similar effects as the second dose of a two-dose regimen)
Why would we need to include an exemption for natural immunity?
Doing so would add additional work to the _already overworked_ health agencies, labs, etc. You'd need to test people to ensure that they have an adequate immune response (at least on par with what the vaccines provides). With unlimited resources and total information, then sure, doing either vaccines or natural immunity would work, assuming that the natural immunity is at least on par with the vaccines. However, given that we don't have unlimited resources nor total information, it's much simpler for the health agencies to ask for everyone that doesn't have a medical exemption to get vaccinated.