We can only test for active infections, not past infections. The disease is still rare enough to not allow for sparse testing but common and infectious enough to spread quickly. The disease is still not fully known. The disease can take up to (or longer) than 14 days to show the symptoms to show that we should test a person. The disease can spread from non-symptomatic persons.

Can't you see how these factors mean that testing 100 people would not lead to a proper representative sample?

I don't think 100 people would be enough to properly and statistically test for a common cold, much less for a disease like this.