For epidemiological purposes, you only need a statistically valid sample, which is much smaller than "everyone".
For medical purposes, you only need to test people who are sick, which is hopefully also much smaller than "everyone".
I've seen it argued that instead of testing the sick (as we currently do), we should be testing individuals who are "high touch" and likely to infect others (even lacking symptoms). Medical staff, first responders. Pharmacy and grocery employees. Bus drivers. Etc. I don't know enough to argue this is a better approach.
That seems to be the main way this is spreading.
The other goal, as others have said, is to isolate, and contact trace the infected. And I add, early detection might also help with treatment, since the scant evidence so far suggests that pharmacological interventions that target the virus might be more effective early on during the infection.
If the goal is to just have everyone get it, but over a longer period of time, it doesn't matter a lot. But that's a shitty goal.
Testing for active infections will help identify people who should self isolate to slow the spread, which is good, but we also should be determining who has antibodies and is able to end self isolation. We need to release some of the social pressure building up and allow people who are ok to go out again to do so.