A distinction needs to be made between test accuracy and test sensitivity. Antigen tests or similar rapid testing may not be as sensitive, so may only detect very high viral loads - but if they are cheap and easy enough to test daily then this is not a problem, so long as they are taken every day.
Apparently viral load ramps up really fast, like hours, until the immune response kicks in, and it is at that high titre that you are most infectious. If everyone tested everyday, and isolated on a positive, then this could all be over by Christmas.