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."

https://link.springer.com/article/10.1007/s10640-020-00466-5