The most obvious one is the breakdown of trust in scientific research. A frequent discussion I would have with another statistics friend of mine was that that anti-vax crowd really isn't as off base as they are more popularly portrayed and if anything, the "trust the science!" rhetoric is more clearly incorrect.

Science should never be taught as dogmatic, but the reproducibility crisis has ultimately fostered a culture where one should not question "established" results (Kahneman famously proclaimed that one "must" accept the results of the unbelievable priming results in his famous book), especially if that one is interested in a long academic career.

The trouble is that some trust is necessary in communicating scientific observations and hypothesis to the general public. It's easy to blame the failure of the public to unify around Covid as based around cultural divides, but the truth is that skepticism around high stakes, hastily done science is well warranted. The trouble is that even when you can step through the research and see the conclusions are sound, the skepticism remains.

However, as someone that has spent a long career using data to understand the world, I suspect the harm directly caused by the wrong conclusions being reached is more minimal than one would think. This is largely because, despite lip service to "data driven decision making", science and statistics very rarely are the prime driver of any policy decision.

I agree wholeheartedly with your conclusion. Science is relevant for those who care about finding the truth, just because they want to know for sure.

But for most people science doesn't really make much difference in how they choose and operate. Knowing the truth doesn't mean you are ready to adapt your behavior.