The first is 'pushed' as it isn't an ideal exposure for raw as 'recommended' by the meter. The 2nd appears far too bright until (using Michaels term from the original ETTR article) normalized. Had the first been optimally exposed, it too would need to be normalized and wouldn't be as noisy. But the main take away is the incorrect concept that higher ISO always produces more noise as the OP implied.
Maybe. But, since the exposures here are the same, the difference must be in the gain applied to the Sensor capture, before the recording of the data, plus any image processing also applied by the camera software. And so this is the result.
I work mostly with professional motion picture digital cameras. Many of these do not process the image before the RAW capture and simply record an image exposed at higher ISO settings/exposure as "darker" or images with less amplitude. It's only in post processing that the exposure is normalized. So, in my case of movie work, the higher ISO image always has more noise. (The gain is applied in post processing). I do wish that my Canon 5Ds would work the same way sometimes
, but it doesn't.
With the movie camera I always know that using a higher ISO will protect more highlights, at the expense of shadows. And vice versa.
And as for exposure strategy, I aim for consistency, and not for "lowest noise". So, generally, I know that if I'm working at ISO 800 (depending on the camera, this is the ISO that provides near equal dynamic range above and below the middle value), I have plenty of data to work with without clipping any wanted highlights. And so, there is little reason for ETTR. Once in a while, on a very high contrast image (typically a day exterior) I'll set the camera to show me the entire range of tones, as opposed to a "preview" that is like a jpg on a still camera. And adjust the exposure accordingly. Or, I'll just use my spot meter. And sometimes, when shooting a very dark scene, I'll shoot at a lower ISO, so that the on set preview is good and dark, but I'lll know that my exposure now will allow me to lighten it a little in post production, without excessive noise, when necessary.
When shooting stills, because my Canon 5Ds adds gain before the RAW recording, when using higher ISO settings, I need to adjust the "exposure compensation" instead of the ISO setting to get the same results or protect the highlights. It would be nice, therefore, if the 5D had a jpg setting for LOG gamma, or maybe "full dynamic range" in order to preview the clipping points. And then, the histograms would be accurate for adjusting exposure in extreme conditions. I think there might be some Sony cameras that allow this in still photography mode, but I'm not sure. These images wouldn't be so good for color correction as the compressed jpgs would fall apart when adding in the missing contrast. This is certainly the case when shooting movies on a Sony A7RII camera in LOG mode and recording the movie in the camera. But if one records to an outboard recorder, this situation improves quite a bit, but is still limited to 8 bits which can cause some banding. But for a purely "exposure preview" plus a RAW capture, for still photography, I'd like to see this feature!