The Exposure Triangle Is Misleading And Unnecessary.

Actually, Live View on a DSLR can potentially have any of the shutter options: zero mechanical curtains, one mechanical curtain, or two mechanical curtains. Live view simply means that the view is from the sensor, and not from the ground glass in an OVF. I don't recall any Live View implementations that were "Silent-only" in a DSLR; the rolling shutter speed of EFCS is too valuable to omit.

Exposure = Light filtered by Aperture filtered by Shutter Speed. That's it.

ISO is basically math to reset the digital numbers that result. There are reasons to do that or not do that (change the math), but neither is without consequence.

What do you mean by "the rolling shutter speed of EFCS is too valuable to omit?" The rolling shutter effect is the same with EFCS and mechanical shutter as both have a mechanical second curtain.
BTW, because of the truncated quote, your post's context is unclear, especially since we do not have a threaded view yet.

Let's do a thought experiment and harken back to the early days of digital photography. The first digital sensor was flown in reconnaissance missions by the US in the mid 1970's. The chip was a CCD imager. In a CCD the charge generated by incident photons was "marched off" the sensor to a follow on processor which performed electronic signal processing to include amplification to support the signal levels required by the follow on ADC and quantization and the data then recorder, communicated back a processing center or potential to an image processing subsystem. The imager like film has a based sensitivity - X photons process Y charge and a dynamic range. The sensitivity translates to minimal detectable signal for follow on processing and is basically equivalent to base fog on film. There is no such thing as an "exposure triangle" that could be manipulated at will. The physics of the device determined the sensitivity and minimal detectable signal that determined the SNR.

Off the CCD chip in the processing chip, the processing is no different than any digital signal processing system. Amplification is used to maximize the performance of the ADC. If the input is amplified - both signal and noise are amplified. The application can make the processed image "brighter," however, at a cost of adding noise since amplifiers are active devices and even low noise amplifiers have a noise figure greater than 0 dB. It was pretty cut and dry - the way you get more sensitivity is not by application but by designing it in the sensor. That is the information content cannot be changed after by the follow on amplification and ADC of the data off the CCD chip. There is no "preputial motion" machine, entropy is always increased and there is no free lunch.

Now along comes advances in semiconductor fabrication and the circuitry of the chip can be integrated onto the sensor chip using CMOS and the CMOS sensor is born. It's no different functionally than the CCD imaging system with the exception the amplification can be accomplished on sensor. That gave birth to the misnomer of the "exposure triangle." While the concept of "exposure triangle" might be useful for cameras that only produce in camera JPEG's - it has little to do with raw capture. If one turns up the application - one amplifies both signal and noise with the addition reduction of SNR by SNRout=SNRin- NFdb where NFdb
is the noise figure of the amplifiers. However, since JPEG's are 8 bit quantized vs 14 bit quantization of the raw the noise floor of the JPEGS is limited from the start.

So yes the way it is talked about on the Internet and in a lot of introductory material the "Exposure Triangle" is misleading and unnecessary for understanding exposure which is simply the light energy captured by the photodetectors. However, it is related to the application and processing to produce the in camera jpegs - the underlying concept is helpful for getting the correct brightness of the in camera jpegs particularly for those who are only interested in 8 bit JPEGs vs. 14 bit raws. It just needs a new name.

Another issue is how to explain the role of ISO in the "exposure triangle." Typical and wrong explanations are: increases grain, increases sensor sensitivity, increases noise, etc. While ISO's role is mainly about regulating brightness, the aperture and the shutter speed have other, more critical functions than brightness.

I think I would just say ISO (above base ISO) is used to compensate (in a number of possible ways) for any shortfall in resulting image brightness due to insufficient exposure brought about by a lack of scene luminance and/or the settings represented by the other two sides of the triangle.

For raw shooters, leaving out considerations about the raw developer and finder brightness, the ISO control represents tradeoff between read noise and clipping susceptibility, and can be set anywhere that the photographer thinks will provide acceptable read noise and clipping.

...and given that the read noise is going down, down, down due to sensors being improved in that regard, the ISO settings above base (2 base settings can be said to be present in dual gain sensors) play a progressively smaller role in helping to suppress the effect of read noise.

Sure, but I think the question was how to explain ISO in terms of the “Exposure Triangle”. How do you explain all this other stuff to someone whose main frame of reference is a faulty triangle?

We need mirrorless cameras where ISO does not affect the EVF brightness (or focus) while still showing usable histograms.

People have been trying to do magic with triangles since at least the time of Pythagoras.
Don Cox

Right OOC, the JPEGs at the higher ISO settings will have more visible noise, because they are brighter and that makes the noise easier to see. Normalize the brightness, and photon noise becomes equally visible, and read noise might be a little bit less visible in the higher ISOs (depending on the camera and specific ISO settings).

I would say that the change in brightness is more relevant than the increase in visible noise.

This is the big problem with these discussions. One person uses "ISO" to refer to the setting on the camera with that number, and another uses it as "ISO exposure index" shortened to "ISO", which is just a way of enumerating the exposure of a middle-grey object. No matter how many times this distinction is made, most people rush right back to using "ISO" without context or qualification. It needs to be qualified in every context; not once in a poster's life history.

If two different words were used for these two different things, we'd have a lot less to talk about, wouldn't we?

It may or it may not, depending on the camera and ISO setting.

There is no requirement, whatsoever, that ISO 102K has more analog gain than ISO 50. None.

However, it is advantageous to use more analog gain (at the earliest stage possible in the signal chain), because there will be less read noise. You do not have to minimize read noise to legitimize a high ISO setting.

D'accord

As I think I said earlier, you have a different conversion with a beginner who is shootings SOOC JPEGs than you have with one who is making raw captures. For raw captures, ISO just isn't that important, unless you get clipping.