> and the small difference in R0 is crude thinking.
Given the reproduction number appears as the base of an exponent, I would not consider the difference "small."
If influenza has a typical R0 of about 2, reducing contacts by 50% would make its growth non-exponential. If covid has a typical R0 of about 2.5, doing the same would require a further 20% reduction of contacts, to 40% of baseline rather than 50%. Since population behaviour and legal restrictions have diminishing returns (eliminating casual contacts first at lower cost, then progressively higher-cost and more essential contacts), this could easily correspond to a large difference in effected (necessary) policy.
> Second, R0 is an estimated value. There are big error bars on all of these estimates -- the overlap is far greater than the 0.5 you're using to claim causality.
I have seen no credible evidence that typical (non-pandemic) influenza has an R0 greater than that of SARS-CoV-2. If you have a citation handy to the contrary, I'd be interested in seeing it. In the meantime, I tried to be generous in my estimation of influenza's R0; even your reference [2] places its central estimate at 1.68.
> Third, rhinovirus has not gone away (estimated R0 Rhinovirus and adenovirus both have mean-estimate R0 greater than that of influenza in your reference [2], so if policy is going to eliminate any of these disease from general circulation then influenza would be the first.
Furthermore, some analysis does show limited evidence of a reduction of rhinovirus cases (https://www.nature.com/articles/d41586-020-03519-3). A confounding factor here, however, is that we don't really have comprehensive like-against-like monitoring for rhinovirus in the way developed nations monitor for influenza. Adenoviruses as a broad category are also not limited to respiratory transmission, so air-focused restrictions would have less effect on these other routes.
Finally, I reiterate that flu has a pronounced seasonal variation, whereas rhinovirus is somewhat less variable. A set of social responses only needs to prevent the flu season from starting to make it "disappear."