The increasing availability of high-resolution Airborne Laser Scanning (ALS) data has expanded the potential for high-fidelity 3D city modeling. At the same time, more and more use cases have surfaced which crucially require these high-fidelity 3D models to derive geometrical building properties in a more straightforward manner. However, standard automatically generated Level of Detail 2 (LoD2) models often fail to accurately capture complex building and roof topologies due to their reliance on overly simplistic geometric primitives, while creating more detailed models typically requires tedious manual editing. To address this gap, we propose a fully automated, data-driven pipeline to generate detailed, LoD3-like roof models utilizing only publicly available LiDAR point clouds and cadastral footprints. Our methodology introduces a robust piecewise affine-linear Mumford-Shah functional for initial point cloud segmentation, followed by discrete graph-cut polygon regularization and a global roof plane estimation step that mathematically encourages watertight, closed seams. Experimental evaluation on the ISPRS Vaihingen benchmark yields a highly competitive planimetric RMSE of 0.27 m. Furthermore, evaluation on a dataset of 109 buildings in M¨unster (Westf.), Germany, demonstrates that our method reduces the mean point-to-surface RMSE by up to 82% in complex urban areas compared to state-provided LoD2 baselines, achieving a superior geometric fit in more than 98% of the evaluated structures and produces visually appealing buildings. Relying on only three fixed global parameters, the proposed deterministic framework offers a highly scalable, mathematically sound path toward detailed, nationwide urban reconstruction.