The most promising plan I've heard along these lines is detailed in a recent episode of This Week in Virology.[2]
This is possible, practical, and affordable.
The technology for fast pregnancy-test style tests for COVID-19 exists right now, and they could cost as little as $1 per test.
The reason these tests aren't being used yet is because of the FDA's misguided requirements for extremely high sensitivity for COVID-19 tests. If these requirements could be relaxed to allow lower-sensitivity tests, then these tests could go out on the market... or, better yet, the government could take over and ensure everyone gets tested with these tests every day for $1 a test.
Even a more limited plan of testing everyone in just highly affected areas would be way better than what we've got now.
[1] - People could, for instance, get tested each morning, and be required to present their daily test results upon arriving at work (or even online, from home, before they start their commute). If they test positive, they just stay home for a couple of weeks and then go back to work when they test negative again. People at work will have confidence all their colleagues (and virtually everyone else out and about) have tested negative.
[2] - Starting at about 6'20" in to episode 640: https://www.microbe.tv/twiv/twiv-640/