Surely with all cameras, whether they are ISO invariant or not, one should attempt to apply ETTR at base ISO for best results, if the required shutter speed and aperture allow it.
Likewise, with all cameras, whether they are ISO invariant or not, one needs to apply the ETTR process regardless of the ISO setting chosen, in order to get the best results, the best results being the lowest noise in shadows and mid-tones, without blowing wanted highlights.
For example, if I'm using a D7000 or D7200, which I would say are pretty close to being ISO invariant cameras, and I decide to use ISO 800, not only because I need a fast shutter speed, or because the light is not good, but also because I want to clearly see what I've shot on the camera's LCD screen, and/or share the images with others in the field, then I still need to apply the ETTR process at ISO 800 in order to achieve the lowest noise and the best review image.
In other words, any exposure which does not push the histogram to the right, whatever the chosen ISO, will result in more image noise.
Where's the confusion? The fact that one might not need to use a high ISO with an ISOless camera, if one doesn't feel the need to be able to clearly view the shots taken on the camera's LCD screen, does not mean that the ETTR principle does not apply if one does choose to raise ISO, rather than underexpose at base ISO.
However, that is not to deny that the ISOless camera has clear advantages. But that is a separate issue
Well stated Ray, but the critical restraints in this situation are the required f/stop and shutter speed. If one is shooting an event in limited light and requires a shutter speed of 1/320 sec to freeze motion and an aperture of f/8 for depth of field, one sets the camera with those parameters. Once this is done, exposure (in lux seconds) is fixed. If the histogram is to the left at base ISO, one could increase the ISO and move the histogram to the right, but this does not change the number of photons collected, but it would brighten the LCD preview. With a non-isoless camera, such as Andrew's Canon, use of a higher ISO will decrease read noise and improve the image. The decrease in read noise with that camera levels out at around ISO 1600, and a further increase in ISO will not improve the read noise, but will decrease highlight headroom and risk blown highlights. Interested readers should refer to Emil's
post.
If the histogram is still to the left at ISO 1600, one could increase the ISO further and move the histogram to the right and get a brighter LCD preview at the risk of blown highlights, but there would otherwise be no improvement in image quality. True ETTR would be to increase the exposure (shutter speed, f/stop), but this is prevented by the chosen restraints on shutter speed and aperture.
With an iso-less camera, one could increase the ISO sufficiently to give a readable LCD preview but not further in order to preserve highlight headroom. I agree with Bart that ETTR is best applied at base ISO. At higher ISO one often can not, because of the above mentioned constraints, move the histogram to the right by increasing exposure. ETTR is a useful concept, but it places undue emphasis on the appearance of the histogram.
Giving maximum exposure would be a better term.
Bill