Video depth estimation is essential for providing 3D scene structure in applications ranging from autonomous driving to mixed reality. Current end-to-end video depth models have established state-of-the-art performance. Although current end-to-end (E2E) models have achieved state-of-the-art performance, they function as tightly coupled systems that suffer from a significant adaptation lag whenever superior single-image depth estimators are released. To mitigate this issue, post-processing methods such as NVDS offer a modular plug-and-play alternative to incorporate any evolving image depth model without retraining. However, existing post-processing methods still struggle to match the efficiency and practicality of E2E systems due to limited speed, accuracy, and RGB reliance. In this work, we revitalize the role of post-processing by proposing VDPP (Video Depth Post-Processing), a framework that improves the speed and accuracy of post-processing methods for video depth estimation. By shifting the paradigm from computationally expensive scene reconstruction to targeted geometric refinement, VDPP operates purely on geometric refinements in low-resolution space. This design achieves exceptional speed (>43.5 FPS on NVIDIA Jetson Orin Nano) while matching the temporal coherence of E2E systems, with dense residual learning driving geometric representations rather than full reconstructions. Furthermore, our VDPP's RGB-free architecture ensures true scalability, enabling immediate integration with any evolving image depth model. Our results demonstrate that VDPP provides a superior balance of speed, accuracy, and memory efficiency, making it the most practical solution for real-time edge deployment. Our project page is at https://github.com/injun-baek/VDPP