This work is a follow-up to an earlier study written by the authors in October 2022 on the "System-level impacts of 24/7 carbon-free electricity procurement in Europe". In this study, we explore how and why space-time load-shifting flexibility can be used to meet high 24/7 carbon-free energy targets, as well as what potential benefits it may offer to 24/7 participants and to the rest of the energy system. To answer these questions, we expand the mathematical model of 24/7 CFE procurement developed in the previous work by incorporating spatial and temporal demand flexibility provided by electricity consumers that follow 24/7 carbon-free energy goals. The space-time flexibility is based on the example of data centers; the findings related to temporal flexibility are generally applicable to a wide range of companies with flexible demand. This study is done in a spirit of open and reproducible research. The whole scientific workflow from the publicly available raw input data to optimized electricity system, visualizations and compilation of this study is available at GitHub. The supplementary materials uploaded to this repository alongside the study include all modelling results in a form of plots and summary CSV files. The study was supported by a grant from Google LLC.