The point isn't to find the people who are negative, but the ones who are positive. When you know who has the disease, you also know who's likely to have it (ie, people they've been near). That allows a strategy of targeted quarantine that is known to be, if properly and effectively implemented, one of the most successful strategies at disease control. Even if you miss some people it still has a decent impact.
At the very least, common sense tells you that response to a disease spread is impossible if you don't have any data. Right now in the UK we have a little under 20,000 known cases (set to rise to about 22-23,000 tomorrow), but it has been estimated that, maybe a week ago, there were already something like 100,000 people infected*. Even if we suppose no new cases since whenever that estimate is from, that's still maybe 80,000 infected patients unaccounted for. The more you don't know about the disease the more of a threat it is.
*Maybe a little less, when Prof. Whitty was making this or a similar estimate. I'm fairly sure that was before the schools were closed, or at least within a day or two.