You don't have to culture anything (if we did we might as well just give up). We use PCR to amplify a known section of the viral genome. With the oligo production capacity in this country alone we could synthesize enough primers test everyone in the country 10 times in a couple of days. That is not the limiting reagent. The limit is either sample prep or sample collection. Actually running the amplification shouldn't be a bottleneck, there are hundreds of thousands of thermal cyclers across the country. In my more cynical moments I might say the bottleneck is that some companies might want to make money from all the tests ....