Counting Coronavirus deaths is hard; one has to figure out whether the patient died from COVID or from a disease caused by COVID or the patient died with COVID.
I think the main reason why government officials count COVID-19 deaths is to see the chance of one with COVID of dying. Usually, officials have medical examiners confirm COVID-19 deaths to create more uniformity and clearer documentation. Also, I think counting COVID deaths can help doctors know where they need to help, and where they do not need to help.