COVID-19 Outbreak (Update: More than 2.9M cases and 132,313 deaths in US)

So, trying to figure out the reticence to having your name recorded at a place of business for the government to use within a limited capacity.

I assume it's caused by the idea that the value in accurate contact tracing is outweighed by some sort of harm caused by the place of business recording your name that might at some point be turned over to the government, right?

I'm curious if this is because the value of accurate contact tracing is not clear enough, or if it's because the fear of harm from the government is high. If it's the latter, are there safeguards and regulations that can be put in place to assuage those concerns?

I assume most people would want to be notified if they were say at a restaurant sitting next to someone who it turns out has COVID-19. If nothing else, so they can be tested and potentially protect loved ones from getting sick. But I might be off in assigning the personal value of contact tracing.