Testing can be a useful tool, but only if people follow through if they test positive. I anticipate that easy availability of tests will just further exacerbate the divide we have in the US. Some people will test, and if they test positive they will stay home and avoid contact with others until they are no longer infectious. These would be the people who already have an appreciation for science and have a sense of social responsibility, and they are almost certainly already vaccinated and boosted. On the other hand there will be a large number of people who don't take the virus seriously, or see it as a badge of patriotism to deny the seriousness of the pandemic, blame it on an anti-Trump conspiracy, believe anonymous hacks from Facebook over their own doctor, etc. These people will not test, are anti-vaccine, and do not give two shits if they infect other people. They love to chant about freedom while demanding that hospitals use unproven or disproven "remedies" such as hydroxychloroquine and ivermectin. Testing half the population while leaving the other half to spread the virus will not accomplish anything that hasn't already been accomplished by making vaccines readily available and free. People who haven't been vaccinated at this point certainly won't test.
For half the population, "Give me freedom or give me death" has mutated into "Give me the freedom to cause your death".