I think if that's what's being suggested that it doesn't sound a very great plan. The standard for something that's contagious/communicable in this way is normally ring containment, which would mean much more targeted testing around confirmed cases, rather than testing every single person in the population.
If it was done during a lockdown with rapid testing, then the testing could focus on healthcare workers, key/essential workers, and anyone entering a hospital or other healthcare setting. Any positive tests can have the 'containment ring' placed around them using quarantine/isolation/testing...and if the people in the contact list for the positive cases obey the quarantine/isolation they don't necessarily need testing.
After that, you just need to test anyone with symptoms and combine that with strict contact tracing. An app would be very useful. I think that during the lockdown period (of my 'plan' that I am developing in my mind) then anyone working should be using a contact tracing app at least during work hours and travel to/from work hours...outside those hours the main risk would be to people in the same living quarters and it would be easy enough to find out who they are, so I think it might suffice to make it voluntary outside of the working/travel hours.
After a few weeks of that, then you could mop up smaller outbreaks with more ring containment for each case/outbreak and the rest of the country could go back to work, preferably maintaining some kind of contact records for a while, but if people are bothered by an app, that could probably be people signing in and out of the workplace or areas within the workplace, maintaining social distancing within the workplace as much as possible, and limiting the number of workers who come into close contact with each other, say by having groups of workers who work together each day and trying to maintain that group through the working week.
My thoughts on developing this 'plan' in my head are based more on the UK, and would have to involve testing anyone entering the country, possibly having anyone entering the country stay isolated for x number of days so that they can have a second test after the first in case there isn't enough antigen to trigger a positive in the first test but that builds up in the next few days. With increased testing protocols they could work out optimum times for those two tests before a person gets the all clear.
I don't know how much of this 'plan' is wishful thinking but it's based on established procedures for overcoming outbreaks. Things like Ebola didn't used to have a vaccine, so these kind of practices were the only thing that could stop outbreaks in their tracks. The major difference here is that we'd have to do this on a national level rather than isolating a few villages and towns in a single region of a nation that doesn't have a lot of national travel, let alone international travel. Even so, they achieved it in the Ebola outbreak a few years ago that was centred in several west African countries. Yes, Ebola's a totally different disease, but it's still the same general principles at work to combat an outbreak of a disease that's communicable by being in close proximity to other people.
So it can be done without vaccines, at least to reduce the size and spread of outbreaks until we get vaccines. And when vaccines do come, if they are also rolled out first to priority groups and then using ring vaccination, then you don't need as much initial supplies of vaccine in order to have a massive effect, so we could roll vaccination out over the globe without needing 7 billion+ doses right at the outset or in the first year. I don't think it's as much about reinventing the wheel but applying these principles in modern nations that aren't used to using contact tracing apps, and never before considered they could have a three-week or longer 'lockdown'. We also need human contact tracing (done by humans) on a scale we aren't used to, but that doesn't mean it can't be built up and achieved.
