The idea of analog neural networks is appealing. I bought Analog VLSI and Neural Systems in 1989 and still have it as a trophy on my bookshelves. My gut feeling says one day analog neural networks will be a thing, if only for the reason of considerable lower power consumption.
I’m not saying that life is analog, DNA is two bits. IMHO life is a mix of Analog & Digital.
It is very difficult to scale digital-analog hybrids, because of amount of DAC-ADC components required.