While recent feed-forward 3D reconstruction models accelerate 3D reconstruction by jointly inferring dense geometry and camera poses in a single pass, their reliance on dense attention imposes a quadratic complexity, creating a prohibitive computational bottleneck that severely limits inference speed. To resolve this, we introduce Speed3R, an end-to-end trainable model inspired by the core principle of Structure-from-Motion: that a sparse set of keypoints is sufficient for robust pose estimation. Speed3R features a dual-branch attention mechanism where a compression branch creates a coarse contextual prior to guide a selection branch, which performs fine-grained attention only on the most informative image tokens. This strategy mimics the efficiency of traditional keypoint matching, achieving a remarkable 12.4x inference speedup on 1000-view sequences, while introducing a minimal, controlled trade-off in geometric accuracy. Validated on standard benchmarks with both VGGT and $π^3$ backbones, our method delivers high-quality reconstructions at a fraction of computational cost, paving the way for efficient large-scale scene modeling.