Statistics for new Covid-19 cases are unreliable.
The issues you mentioned would still result in an under-reporting of actual positives. Unreliable tests would encourage spread of the virus and complicate contact tracing.
Provide proof that people are being reported as dying from the virus erroneously. That data is from hospitals managing cases. It seems incredibly unlikely that there was no involvement from the virus when someone suffering from it dies with a comorbid condition.
People are relying on imperfect data because they live in the real world and care about their families and human lives in general.
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