Isn't it still a problem if someone takes a test on day N and it comes back negative, but their viral load increases over the next few days and they begin sprea

Isn't it still a problem if someone takes a test on day N and it comes back negative, but their viral load increases over the next few days and they begin spreading the virus on day N+3? Many people in such a situation would read the test as "I'm in the clear for a while" and might engage in close contact with friends and family members that would put them at risk.