The greater the KL-divergence, the longer the codeword of Shannon information, the longer the response time. Natural selection would choose rapid responses, so the KL-divergence is minimized: the probability density of the fluctuating intracellular ion concentration is kept as close to the mostly-constant probability density of the extracellular concentration as possible.
The huge range of different perturbations leading to intracellular ion concentration changes would increase the evolutionary pressure for complex and diverse ion channels under this principle