In this paper, we propose a rate-distributed linearly constrained minimum variance (LCMV) beamformer for joint noise reduction and spatial cue preservation for assistive hearing in wireless acoustic sensor networks (WASNs). The WASN can consist of wireless communicating hearing aids, extended with additional wireless microphones. Due to the fact that each sensor node has a limited power budget, it is essential to consider the energy usage when designing algorithms for such WASNs. As the energy usage in terms of data transmission is directly affected by the communication rate, the proposed method optimally distributes the bit rate for each microphone node. The rate distribution is obtained by minimizing the total transmission costs under constraints on the noise reduction performance and spatial cue preservation of interfering sources. In contrast to \textit{sensor selection}, i.e., binary decisions on the usefulness of a node, rate distribution allows for soft decisions, and, will lead to more degrees of freedom for joint noise reduction and spatial cue preservation than sensor selection. Numerical results show that given a certain noise reduction requirement, the proposed method displays improved energy efficiency and can preserve the spatial cues of more interferers compared to sensor selection approaches.