[Question] In the absence of advanced medical interventions, would the impact of infectious diseases on human society increase overtime?

Epistemological status: I believe this is wrong, but I would like to know why

I have this question because the conclusion

--”If the human society do not have access to medical interventions, the burden of infectious diseases would increase over time as more types of pathogens are established in the population”

seems to follow from the below assumptions (I think most of them are correct, maybe with caveats):

1: Smallpox is the only (major?) infectious disease that we have eradicated. It would be an impossible feat in the absence of modern healthcare, and replicating the success with other infectious diseases would be more difficult or straightaway impossible.

2: New infectious diseases become established in the human population overtime through zoonosis (and maybe other pathways too)

3: Being infected by pathogen A confers some immunity to A but does not offer protection to infection by pathogen B.

Combining all 3, it seems to me that as more types of pathogens become established in the human population, the burden of infectious disease on each individual will increase.

As an oversimplified example, suppose that immunity of influenza does not protect an individual from infection by SARS-covid-2 and vice versa.

Prior to 2020, there is a “flu season” each year as the population’s immunity to influenza waxes and wanes.

If we did not implement any public health measures during the covid pandemic, the spread of influenza would continue unchanged due to the absence of cross-immunity.

Then after covid reached a steady state in the human population (perhaps a seasonal pattern), each year a human individual will have to contend with “SARS-covid-2 season” on top of “the flu season” (which continues at the same level as pre-2020), and this I believe means an increase of the burden of infectious diseases on humanity.

I think I’m missing something here and this conclusion is wrong, but I can’t tell why.