So as the other comments are going to say, this doesn't work because of noise and linearity issues, temperature sensitivity etc. But there is one place which is trying to bring this back: there have been attempts to do analogue neural networks, where getting the exact value isn't so critical and the system has a certain amount of noise correction by its very operation.

The last greatest flight of pure-analogue control systems was Concorde!

(There are a few places where multiple signalling levels are widely used; things like MLC flash and some of the faster ethernet specs. I don't think anyone's dared to do arithmetic on them before quantizing to digital, though.)

If you go that direction might as well go full analog computing, I suspect quantizing into 10 values would not bring much benefits

Traditionally you have error correction issues which require frequent and specific manual tuning on a case by case basis. This was the age of the analog machine.

However there are some recent works which have introduced compromises to continue to do just that: https://www.nature.com/articles/s41928-018-0100-6

I understand enough to think the proposal sounds reasonable, but not enough to know why it is apparently, in fact, unreasonable.

Digital logic is built from amplifiers with the gain set right up, so that any voltage above the threshold goes to max and any voltage below goes to zero. Very little tuning is needed to get a working circuit, compared to multi-level or analog circuitry. In CMOS, current basically only flows when the circuit is switching between two states, whereas in an analogue circuit it flows all the time, so digital logic can be more efficient. In digital signal transmission, “eye diagrams” are used to visualise the quality of the signal: the eye is the gap between low and high and it needs to be clearly open for receivers to be able to detect the signal with decent integrity. https://www.onsemi.com/pub/Collateral/AND9075-D.PDF