Federated Learning (FL) offers a paradigm for collaborative machine learning model training among clients, preserving data privacy by avoiding direct data sharing. However, the gradient information exchanged in FL has been shown to be vulnerable to Gradient Inversion Attacks (GIA), which can reconstruct sensitive user data. To counter these threats, various privacy-enhancing technologies like Secure Multi-party Computing (SMC), Homomorphic Encryption (HE), and Differential Privacy (DP) have been integrated into FL. While effective, these methods often introduce significant trade-offs between privacy and model utility. By revisiting the key to privacy exposure in FL under GIA, which lies in the frequent sharing of model gradients that contain private data, we take a new perspective by designing a novel privacy-preserving FL framework that effectively ``breaks the direct connection'' between the shared parameters and the local private data to defend against GIA. Our proposed framework, HyperFL++, leverages hypernetworks to generate local model parameters, where only the hypernetwork parameters are aggregated by the server. To ensure practicality, HyperFL++ incorporates a Row-wise Kronecker Decomposition (RKD) to mitigate the memory and communication overhead from the hypernetwork. Comprehensive theoretical analysis and extensive experiments validate our method's effectiveness in protecting data privacy while maintaining high model utility. Our code is available at https://github.com/Pengxin-Guo/HyperFL/tree/hyperfl%2B%2B.

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