The title is a bit misleading IMHO. It's more like analog vs digital.
After all, from an electrical point of view they're usually just potentiometers and you can build them either as rotary or as linear potentiometers, but it's just a wiper on a resistive conductive track... (of course there are exceptions that work differently and use hall effect or optical sensors).
The article only talks about the actual circuit that is behind that potentiometer.
Having built some MIDI controllers myself in the past, I noticed that rotary potentiometers allow you to better "decouple" arm/shoulder movements from hand/finger movements. I.e. when you're standing and and holding that knob, It's easier to make precise adjustments when there's a rotary knob you can "hold on to" and slowly twist your fingers, whereas with a linear potentiometer I usually have to keep a finger on the surface next to the knob to "compensate" for involuntary movements coming from my body and arm...
Yes, this is the same for controls in a car. Whoever thought a touch display was the way to go? Our old car had twisty-nobs that you could feel direction already on the grip. No need to look on the symbols what they adjusted. Our "modern" car has still twisty-nobs (we made extra sure of that) but you can't feel the direction because they are perfectly round with a tiny tiny nob for direction. Why do I get the impression development goes backwards?
The hardware is much cheaper, but it is also way cheaper to engineer, and because a touchscreen is a very one-dimensional interface, many questions don't even need to be asked. There's no texture, shape or feedback in a touchscreen, for example.
Are there physical controls that mount on a digitizer? E.g. instead of a rotary dial on a potentiometer, the bottom sits on a digitizer that can translate the "touch" event into circular motion. Same with buttons, like with a keyboard membrane, but capacitive. Wouldn't that be cheaper?
That’s not addressing the right issue. Encoders and switches are not the expensive parts. What’s expensive is designing the dashboard with precise holes, before you actually start the manufacturing process, lining up the component with the hole and cap, making sure they actually work etc. Compare that to a dashboard of the new Tesla robo taxi, which basically has a complexity of a TV mount.
But you don't need to line up the holes if you can just plonk the component down anywhere and then program the software with the locations of the components after the fact.
This is also my experience. I'm not a DJ but I perform live electronic music using various MIDI controllers. If I quickly want to add or remove a sound, like a kick drum, to/from the mix, a slider is best. If I need fine control over a parameter, like a low-pass filter frequency, a rotary controller is usually better for the reasons you mentioned.
As alluded to in the article, rotary vs. linear seems to be a proxy for the circuit which actually influences the sound. I would think that anyone claiming "mixers with rotaries always sound better" does not fully understand how they work. There's a lot of those kind of claims in the music scene.
The article only talks about the actual circuit that is behind that potentiometer.
Having built some MIDI controllers myself in the past, I noticed that rotary potentiometers allow you to better "decouple" arm/shoulder movements from hand/finger movements. I.e. when you're standing and and holding that knob, It's easier to make precise adjustments when there's a rotary knob you can "hold on to" and slowly twist your fingers, whereas with a linear potentiometer I usually have to keep a finger on the surface next to the knob to "compensate" for involuntary movements coming from my body and arm...