Tropical cyclone-induced storm surge is a major coastal risk which will be further amplified by rising sea levels under global warming. The surge-induced floodplains are commonly modeled using a two-step approach by first producing coastal water levels which are, secondly, translated into inundated areas. Here, we evaluate an alternative approach where ocean dynamics and coastal inundation are modeled in a single step using the open-source solver GeoClaw that accounts for the event-specific variation over time of flood drivers. We compute the surge-induced flood extents for a global set of 71 storms from 2000-2019. We show that GeoClaw better reproduces satellite observations and high water marks than two different common modeling approaches that lack a process-based representation of inundation dynamics: a state-of-the-art two-step approach combining a full-scale ocean dynamics with a static (bathtub-type) inundation model and a lightweight approach that directly translates parametric tropical cyclone wind fields into inundation maps using statistical relationships. GeoClaw does not reach the performance of the ocean dynamics model in reproducing coastal water levels, but this deficiency is overcompensated by the dynamic modeling of inundated areas. The computational efficiency of the one-step approach opens up new perspectives for global assessments of coastal risks from tropical cyclones.