In user-generated-content (UGC) applications, non-expert users often rely on image-to-3D generative models to create 3D assets. In this context, primitive-based shape abstraction offers a promising solution for UGC scenarios by compressing high-resolution meshes into compact, editable representations. Towards this end, effective shape abstraction must therefore be structure-aware, characterized by low overlap between primitives, part-aware alignment, and primitive compactness. We present Light-SQ, a novel superquadric-based optimization framework that explicitly emphasizes structure-awareness from three aspects. (a) We introduce SDF carving to iteratively udpate the target signed distance field, discouraging overlap between primitives. (b) We propose a block-regrow-fill strategy guided by structure-aware volumetric decomposition, enabling structural partitioning to drive primitive placement. (c) We implement adaptive residual pruning based on SDF update history to surpress over-segmentation and ensure compact results. In addition, Light-SQ supports multiscale fitting, enabling localized refinement to preserve fine geometric details. To evaluate our method, we introduce 3DGen-Prim, a benchmark extending 3DGen-Bench with new metrics for both reconstruction quality and primitive-level editability. Extensive experiments demonstrate that Light-SQ enables efficient, high-fidelity, and editable shape abstraction with superquadrics for complex generated geometry, advancing the feasibility of 3D UGC creation. Project Page: https://johann.wang/Light-SQ/ .