If you pass the output of a bandpass filter directly to a lowpass filter, you would often get a zero signal (depending on cutoff frequencies).
I believe that the filterbank->rectifier->lowpass filter is typically chosen to have a smooth, low-rate energy/power measure, where LPF cutoff << BPF bandwidth. Having a BPF and a LPF in series with no intermediate processing makes little sense for me, then you could just as well pull all of the work with the BPF.
So perhaps your question can be rewritten as "why dont we just hook up a bank of bandpass filters directly to stimulate our hearing nerves?". When you replace biologic parts with artificial parts, it makes sense to try to mimic (our understanding of) the parts that we are replacing.
This text seems relevant: "Each output channel is half-wave rectiﬁed to simulate the output of the inner hair cells along the length of the cochlea."
Auditory Sparse Coding