The privacy-focused concept of Federated Learning (FL) allows local data processing without disclosing patients’ health details to a central server. However, its vulnerability to privacy breaches through shared model weights and susceptibility to a single point of failure remain concerns. Energy constraints of Wireless Body Area Networks (WBANs) necessitate considering computation and transmission energy in the FL process. Thus, this article introduces a smart healthcare system prioritizing energy efficiency and privacy through a blockchain-backed FL model. Yet, WBAN users might be unwilling to share data without adequate incentives, and miners might hesitate due to the high energy usage associated with maintaining the blockchain. Therefore, an optimization problem is formulated to maximize system utility while considering energy, WBAN incentives, miner revenue, and FL loss. A computationally efficient stable matching-based algorithm is proposed for optimizing utility via associating WBANs and miners. Associated WBANs use Quantized Neural Networks (QNNs) to minimize computation energy. Moreover, this work integrates Differential Privacy (DP) and Homomorphic Encryption (HE) mechanisms to prevent information leakage by adding noise to gradients before updating model weights and encrypting consequences before transmitting them to miners. Real-world experiments validate the framework, yielding an average of 15.1%, 9.03%, and 15.35% improvements over existing methods.