I'm not arguing it's not complex or that a lot of factors go into the response. I am however suggesting your original claim that non pharmaceutical interventions had little effect is demonstrably false. Comparing the 1 death in Taiwan and the to tens of thousands in the UK, including strong quarantines and contact tracing quite obviously had an impact.
Though likely a much smaller impact than other factors such as cross-immunity from previous HCoV epidemics such as SARS and MERS.
There are no studies which have found statistically significant links between political measures and excess COVID deaths.
From the conclusions section:
“Regarding government's actions (i.e., containment and stringency index), no association was found with the outcome, suggesting that the other studied factors were more important in the Covid-19 mortality than political measures implemented to fight the virus, except for the economic support index.”
SARS and MERS didn't reach anywhere close to spreading through the population, so cross immunity (if it's strong, which we don't know), wouldn't have done much. The fact that you bring that up as a rebuttal is telling.
One difference with those is that their governance and infrastructure to tackle a pandemic already existed, which counts. You could write that off to existing 'public health', as you have tried to stretch from the paper, but that is a disingenuous of that research.
A quick search implies that you are also not looking very hard to find studies that don't find linkages. "The results presented in this paper suggest that policy interventions may well explain the majority of cross-country variation in officially reported Covid-19 deaths."
This is an interesting study which takes a wide variety of factors into account - https://www.frontiersin.org/articles/10.3389/fpubh.2020.6043...