Compared to other self-propelled particles, pedestrians are able to anticipate, which gives them an edge in avoiding collisions and navigating in cluttered spaces. These capabilities are impaired by digital distraction through smartphones, a growing safety concern. To capture these features, we put forward a continuous agent-based model hinging on a transparent delineation of a decisionmaking process and a mechanical layer that handles contacts and collisions. In the decisional layer, each agent autonomously selects their desired velocity as the optimum of a perceived cost, notably balancing the will to move forward (described by a floor field) with the bio-mechanical cost of walking and the risk of collision, assessed by an anticipated time-to-collision. Altogether, the model includes less than a dozen parameters, most of which are fit using independent experimental data. Numerical simulations demonstrate the versatility of the approach, which succeeds in reproducing empirical observations in extremely diverse scenarios, often quantitatively, with a single set of parameters. These scenarios range from collision avoidance involving one, two, or more agents to collective flow properties in unidirectional and bidirectional settings and to the dynamics of evacuation through a bottleneck, where contact forces are directly accessible. Remarkably, a straightforward transcription of digital distraction into the model, by reducing the frequency of decisional updates, suffices to replicate the enhanced chaoticity of the flow, with more frequent sudden turns, observed experimentally when 'smartphone-walking' pedestrians are brought in. Finally, the conceptual transparency of the model makes it easy to pinpoint the origin of some deficiencies, notably its shortsighted account of anticipation (when agents have to cross a group of people) and the disk-like pedestrian shape (when very dense crowds are considered). Our work thus clarifies the singular position of pedestrian crowds in the midst of active-matter systems.