>Which is why the argument makes no sense. Either digital systems add something new and unique to the mix, or they don't.I'm sorry but this runs counter the observed historical reality.
For reference, consider data transmission interfaces (USB, SCSI, memory busses, display interfaces, etc): "Is parallel better than serial? Is serial better than parallel?". The history clearly indicates that, every few generation of interfaces there's a big switch-over between parallel and serial, and back, and fore again. The approaches simply have different trade-offs, and at different point of evolution of our understanding and available technology it makes sense to pick one over another. Neither of them is inherently "ultimately better".
Likewise digital vs analog computing. It used to be[1] that analog (calculations and computations) ruled the day. In case we forgot already, there were not only analog (mechanical and electrical and electronic) programmable computers and fixed-function, complex calculators, but many an everyday object are analog electronic calculators in time and frequency domains. Cue the humble superheterodyne radio, and the analog color TV. Cybernetics used to be a thing, too.
Then came the digital electronic computation, which allowed us to translate lambda-calculus theory verbatim into discrete bits (sorry!) of control words and data. However digital is a leaky abstraction over switching electronics [2]; all the transistors aren't digital, and - Moore's law notwithstanding - digital view of analog semiconductors is modern equivalent of squaring a circle. Or describing astronomy with ever more epicycles. It works, but at the cost of the ever-growing complexity, and a bit of suspension of disbelief.
We already are having renaissance of continuous-valued computation: the present day crop of early quantum computers. Both the computing elements (quantum gates) and also the control programs and data are in the complex number domain.
On the other end of the spectrum, we're using ever more neural networks, which are analog abstractions over our digital computers. At some point somebody will start asking questions. Maybe even invent (or make feasible) the long-awaited memristor.
I'm sure we'll be shifting back to digital in a few decades though.
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[1] glossing over discrete computation approach of the early pioneers like Charles Babbage
[2] and switching electronics, whether semiconducting or valve-based, is merely a leaky abstraction over high-gain analog amplification, but I digress