During the COVID-19 crisis, the French National Institute of Statistics and Economic Studies (INSEE) used aggregated and anonymous counting indicators based on network signaling data of three of the four mobile network operators (MNOs) in France to measure the distribution of population over the territory during and after the lockdown and to enrich the toolbox of high-frequency economic indicators used to follow the economic situation. INSEE’s strategy was to combine information coming from different MNOs together with the national population estimates it usually produces in order to get more reliable statistics and to measure uncertainty. This paper relates and situates this initiative within the long-term methodological collaborations between INSEE and different MNOs, and INSEE, Eurostat, and some other European national statistical institutes (NSIs). These collaborations aim at constructing experimental official statistics on the population present in a given place and at a given time, from mobile phone data (MPD). The COVID-19 initiative has confirmed that more methodological investments are needed to increase relevance of and trust in these data. We suggest this methodological work should be done in close collaboration between NSIs, MNOs, and research, to construct the most reliable statistical processes. This work requires exploiting raw data, so the research and statistical exemptions present in the general data protection regulation (GDPR) should be introduced as well in the new e-privacy regulation. We also raise the challenges of articulating commercial and public interest rationales and articulating transparency and commercial secrets requirements. Finally, it elaborates on the role NSIs can play in the MPD valorization ecosystem.