That might work, although I think there are two limitations:
1) Hearing aids have a 10ms latency budget. So no matter how much processing they can do, they're limited by how many samples they can look ahead and that limits the design of the filters. The brain can presumably look ahead further to separate sound streams so I think it's pretty impressive that ideal binary masking works.
2) Hearing aids have a power budget. The ones I've looked at achieve low power by running a FIR filter in hardware to shape the sound while a DSP classifies the sound and adjust the filter taps. The DSP doesn't have to run at the same rate as the filter. That seems well matched to the binary filter approach. Likewise features extraction might not run at the same rate as the DNN.
The latency and power issues can probably be fixed, assuming a good end-to-end model, by using model distillation into a wide shallow net using low-precision or even binary operations. I don't know if that would be enough - we've seen multiple order of magnitude decreases in compute requirements (think about style transfer going from hours on top-end Titan GPUs to realtime on mobile phones) but the usual target is mobile smartphones which at least have a GPU, while it seems unlikely any hearing aids will have GPUs anytime soon... I suppose a good enough squashed low-precision model could be turned into an ASIC.
Not to detract from your larger point but AFAIK the style transfer thing is different. If you're willing to hardcode the style into the net you can go realtime, but the original style transfer paper is able to do different styles without retraining. So they're different algorithms. Unless the SOTA has changed recently.
You shouldn't need to hardcode the style if you provide the style as an additional datapoint for it to condition on. But this doesn't really matter since for fun mobile applications it's fine to pick from 20 or 50 pretrained styles, and likewise for hearing aids.
1) Hearing aids have a 10ms latency budget. So no matter how much processing they can do, they're limited by how many samples they can look ahead and that limits the design of the filters. The brain can presumably look ahead further to separate sound streams so I think it's pretty impressive that ideal binary masking works.
2) Hearing aids have a power budget. The ones I've looked at achieve low power by running a FIR filter in hardware to shape the sound while a DSP classifies the sound and adjust the filter taps. The DSP doesn't have to run at the same rate as the filter. That seems well matched to the binary filter approach. Likewise features extraction might not run at the same rate as the DNN.