if we knew the identities of all or most of the current cases, we could isolate them, trace their contacts, and thus slow the spread giving our systems more time to prepare by letting us allocate resources more effectively instead of reacting to critical cases only.

here is an analysis of the percentage of contacts we would have to trace (paramerized on R0), to stop the spread entirely. https://www.thelancet.com/journals/langlo/article/PIIS2214-1...

(We're probably past that point now, though)