I don't think I've ever seen a touch screen with only two wires. For one thing, even power requires two wires, not one. Data for a touch screen typically requires more than one wire as well, especially considering there are two completely distinct types of data a touchscreen must transmit, those being display output and touch input.
Most touch screens I'm aware of have wire connections more like this:
> Usually they're replacing a lot more than 2 buttons/knobs.
Not usually. Other than the Tesla, most cars retain almost all of their knobs/buttons in addition to the touch screen. In fact, the linked article in the OP says they're basically replacing the touch screen input with a single volume knob that lets you additional tilt and push it. Other cars, like BMW with the iDrive, usually have a single knob that lets you rotate and scroll through menus and push to select. Granted, it's not a simple knob, since it requires multiple degrees of input, but even a plastic knob that allows rotating, tilting, and pushing is probably cheaper than a touch screen when shared across models and mass produced.
I still think the bigger savings is probably the software updates required to constantly support and make your vehicle's physical input compatible with every new update of Android Auto and Apple Car Play, which the auto-makers have no control over and can only ever play catch-up. At least with a touch screen, they know that's where the Android and Apple engineers spend their own time making compatible.
The other place it probably saves is designing and laying out the interior, since it's easier to design an interior with fewer purpose-focused inputs. I'm not sure though if the touch screen would actually be easier though, since it can't be broken up across different small areas, and the entire thing has to be within both reach and active field of view. Especially the screens on top of the dash, since those often are designed to retract, which means the space they retract into needs to be designed around the HVAC and electrical systems between the firewall and dash.
Either way, both of these savings though would be on the design and engineering side, not the bill of materials.
Most touch screens I'm aware of have wire connections more like this [...]
That link is to a toy touchscreen. Are we counting every strand of metal as its own wire now? I think the power and the data cables are each bundles of lots of such strands, and no car manufacturers worry about the individual strands because each cable plugs into the circuit board as a cohesive unit, like: https://www.alibaba.com/product-detail/Customized-odm-15-6-i...
(First Google result for "touchscreen alibaba", it's not like this is an obscure, rarely used configuration.)
Either way, both of these savings though would be on the design and engineering side, not the bill of materials.
¯\_(ツ)_/¯ Those sound like good points to me, but I don't know anything about this stuff.
I do know about this stuff (currently work for one OEM and have worked for 2 others) and you're exactly right.
Something that hasn't even been mentioned is all the meetings, documentation, coordination between people that work on the components that have to interface with each other. That labor is significantly reduced when you offload most of that to the touch screen because some of that interface can now be done by the same person without any meetings. That's not just cost savings, it's also time savings, which is part of why Tesla was able to bring the model 3 to market so fast (fast at least in the car world).
That said, I much prefer tactile controls. I recently moved from a BMW to a Volvo had the BMW had physical controls for most common functions while the Volvo only has a handful of buttons and one knob for volume. It's a pretty good balance, but I do miss a few buttons and more could be done on the touchscreen to ease that longing (such as customizable shortcuts).
Cadillac is starting to go back to more tactile controls because they've learned how terrible it is without any (my wife has a CTS so I completely understand why they're doing it -- it is awful). I hope Audi changes course too.
