> Do any controllers have a twistable thumbstick?
Yes, several. For example, the main knob on the Komplete Kontrol S-series MIDI controllers (https://www.native-instruments.com/en/products/komplete/keyb...) combines a rotary encoder with four axis directional input, a push button and an LED indicator ring. I have an S61 and the implementation of the knob is delightfully intuitive, responsive and functional. To be clear, this implementation is not a joystick on a ball base with twistable knob, it's a flush-mounted knob that can be slightly nudged up, down, left or right with a single, satisfying click in each direction. I'd recommend trying it yourself, if only there were still any music stores that put a range of high-end midi controller keyboards out where customers could, you know, touch them.
I actually came here to suggest the same idea for the EuroKnob. The four axis directional input is basically a D-Pad module commonly used in game controllers. I find this kind of rotary knob + directional input control to be very effective. However, there's one critical caveat. It's apparently possible to implement this kind of control poorly because I've also seen a couple devices where the implementation is as bad as the S61's is great. It probably just requires a certain degree of engineering finesse to nail a good combination of responsiveness and tactile feedback.
> You could mount it on a linear pot/slider.
As much as I like and agree with your first thought, I've actually seen the idea of a rotary knob combined with a linear slider - although it's extremely rare. Having touched one myself I can confirm the reason it's rare is that it's not just bad - it's uniquely bad. By which I mean the combination of two controls which each work so well on their own into one combined control, is unexpectedly awful. I was unfortunate enough to try one first-hand (so to speak) at a tiny booth buried in the back of some long-forgotten NAMM show in the days when Cubase was still being demoed on an Atari ST. There was a bespoke mixer from a company I'd never heard of with rotary knobs on their mixer's sliders. I'm pretty sure when I tried to adjust the two parameters at the same time I may have reflexively pulled my hand back and uttered "Ugh!"
Usually I'm polite when trying out some novel interface idea but there must be something 'special' about trying to combine two very precise but divergent proportional motions on two different arm joins (wrist & elbow) at the same time that's deeply unnatural. It felt so weirdly wrong that I suspect some human factors kinesiologist has probably written an award-winning paper about how humans evolved to never, ever do this. But hey, one out of two ideas is still a great day! :-)