We argue that frequent sampling of the fraction of a priori non-symptomatic but infectious humans (either by random or cohort testing) significantly improves the management of the COVID-19 pandemic, when compared to intervention strategies relying on data from symptomatic cases only. This is because such sampling measures the incidence of the disease, the key variable controlled by restrictive measures, and thus anticipates the load on the healthcare system due to progression of the disease. The frequent testing of non-symptomatic infectiousness will (i) significantly improve the predictability of the pandemic, (ii) allow informed and optimized decisions on how to modify restrictive measures, with shorter delay times than the present ones, and (iii) enable the real-time assessment of the efficiency of new means to reduce transmission rates. These advantages are quantified by considering a feedback and control model of mitigation where the feedback is derived from the evolution of the daily measured prevalence. While the basic model we propose aggregates data for the entire population of a country such as Switzerland, we point out generalizations which account for hot spots which are analogous to Anderson-localized regions in the theory of diffusion in random media.