Overall, I think the things you're saying about the expressiveness and power of digital logic are valid, but I don't think they really apply here when the logic is so minimal and could in theory be removed entirely.
I can find no examples of an acoustically-based mechanical timekeeping mechanism. If you're aware of any I'd be interested in seeing them.
I can also remember when mechanical stopwatches were still A Thing, used in sport timing when I was a wee'un. I suspect that these were the highest-precision timepieces reasonably mass-produced (and likely expensive nonetheless), and they could reach 1/10th second accuracy. Far cheaper digital stopwatches came available shortly after, were less expensive, and had 1/100th s accuracy. They could easily have recorded to greater accuracy but the limits of human perception and reaction would have made that redundant.
Current prices seem to range from ~US25 to ~$150 for mechanical stopwatches, versus ~$2 to $20 for digital electronic stopwatches, going off Amazon.
Even now, timed events are generally only measured and judged to 1/100th of a second, given that unavoidable variances (e.g., in track or lane length for track or swimming events, or course lengths for others) would introduce variability not strictly addressed by an athlete's capability.
But the only electronic part you actually need is a toggle (well, a handful of them in series). That doesn't increase your capabilities beyond gears, except that you can pick up a faster signal (and then the only thing you can do with it is slow it back down).
> A digital watch can fundamentally be implemented entirely in software, in ways that I'll venture a hardware watch cannot be.
If you say hardware can't truly be represented, then neither can the quartz crystal, and I would argue that output hardware can't truly be represented either. So the two things you're doing entirely in software are the conversion from 32kHz down to 1Hz, and the conversion from 1Hz to a series of digits.
But the type of watch we're talking about doesn't have a digits display so discard that.
Now the only thing you're doing in software is dividing by 2 a few times, maybe also dividing by 60. That's not beyond the capabilities of a simple mechanical system. There's no need to have "software" involved either. "Software" is orders of magnitude more complex than dividing by 2.
Or, another way to look at things: A watch just like a quartz watch can be implemented completely in hardware, if you put in a """crystal""" that wiggles at 8Hz instead of 32768Hz.
I see your point about speed being a meaningful difference in many areas, but in this case the only thing done at high speed is slow it back down.
> There's also the point that gears ... rotate continuously, rather than discretely. We can modify that (e.g., with cams or similar designs), but there's still that continous rotational motion at core.
The gears right at the core of a mechanical clock are moving in pulses. It's not very far off from what the transistors or vacuum tubes would be doing.