I'm not a clinician or public health policymaker, so I'm operating on the balance of probabilities rather than a p=0.05 standard.
If you consider the influenza estimate independent of equivalent estimates for covid, then there's a substantially greater than 50% chance that influenza's R0 is meaningfully smaller than that of the flu. If the estimates are partially dependent (i.e. methodology that gives a larger estimate for influenza would also give a larger estimate for covid), then that chance goes up further.
Moreover, we also have evidence in the actual observations of epidemic dynamics. Over the southern hemisphere fall of 2020 (northern hemisphere spring), covid cases increased more rapidly than influenza cases in countries that were entering their flu seasons. That's compelling-to-me evidence that covid in fact has a larger basic reproductive number, whether that be due to a fundamental difference in the virus or just the effects of low baseline immunity.
Now, your idea that the particular set of policy restrictions may be more effective against influenza than covid is very interesting. There's a basic horse sense to it, as well, since policymakers were largely operating from a playbook written for a flu pandemic. However, I do not think that "more effective" is a necessary component of the argument; "at least as effective" will do just as well given influenza's low baseline prevalence (out of season).
Remember, my original point upthread was not to explain every bit of the relative epidemic curves, but instead to claim that we really ought not be surprised by the difference. I see little need to resort to specialized theories to explain the broad outline, even though I'm sure they will be helpful in the details.