Recent progress in scaling large models has motivated recommender systems to increase model depth and capacity to better leverage massive behavioral data. However, recommendation inputs are high-dimensional and extremely sparse, and simply scaling dense backbones (e.g., deep MLPs) often yields diminishing returns or even performance degradation. Our analysis of industrial CTR models reveals a phenomenon of implicit connection sparsity: most learned connection weights tend towards zero, while only a small fraction remain prominent. This indicates a structural mismatch between dense connectivity and sparse recommendation data; by compelling the model to process vast low-utility connections instead of valid signals, the dense architecture itself becomes the primary bottleneck to effective pattern modeling. We propose SSR (Explicit Sparsity for Scalable Recommendation), a framework that incorporates sparsity explicitly into the architecture. SSR employs a multi-view ''filter-then-fuse'' mechanism, decomposing inputs into parallel views for dimension-level sparse filtering followed by dense fusion. Specifically, we realize the sparsity via two strategies: a Static Random Filter that achieves efficient structural sparsity via fixed dimension subsets, and Iterative Competitive Sparse (ICS), a differentiable dynamic mechanism that employs bio-inspired competition to adaptively retain high-response dimensions. Experiments on three public datasets and a billion-scale industrial dataset from AliExpress (a global e-commerce platform) show that SSR outperforms state-of-the-art baselines under similar budgets. Crucially, SSR exhibits superior scalability, delivering continuous performance gains where dense models saturate. The code is available at https://github.com/Atticus666/SSRNet.