This explanation does not quite make sense to me.
If you first set your exposure such that your flare is 7 stops below full well, and your brightest image pixel is 1 stop below full well, you may use ETTR to expose one more stop such that your brightest pixel is just at full well. Your flare is now 6 stops below full well but you have changed nothing about the ratio between image and flare. You have increased the signal to noise ratio in the midtones, let's say 3-5 stops below full well and that is good. You can now reset your black point in post to 6 stops below full well and you don't see the flare anymore.
If your exposure already clips some highlights, you normally do not apply ETTR unless you think that further clipping those highlights is not detrimental to the picture. If that is the case, let's say you have one more stop of highlights that you can clip (let's say, specular highlights). Your flare is at -7 stops as before. After increasing exposure, your flare is at -6 stops and your brightest image-relevant pixel is just at full well. Again, you have maximized signal to noise ratio and you may reset your black point in post.
I fail to imagine a situation where you would not want to use ETTR.
If you set your exposure so flare is seven stops below FWC, and then say, "I will ETTR" and increase flare to six stops below FWC the
darkest pixel in the image, that in a flare free image was black, is one stop brighter. The
maximum dynamic range has, therefore, been reduced by one stop. Sure, if the brightest pixel was one stop below FWC and is now just at FWC the dynamic range of your image is not affected. Photography has always been easy when the scene dynamic range is less than the recording medium. But if the scene dynamic range is the same as or greater than the dynamic range of the sensor - which is hardly uncommon - you
have lost a stop of dynamic range because of the increased flare. You can make the flare-affected pixels black again, but you can't recover the lost information.
Flare is a form of noise, but like dark noise rather than photon noise, which is how you are treating it: it is added to every pixel, and its effect is greater in darker pixels. If you increase exposure one stop you double the amount of light. But the image light is not evenly distributed across the sensor. Some parts of the image are bright and some are black: some parts of the sensor get a lot of light and some get none. But the flare light
is evenly distributed across the sensor. So although the ratio of flare light to image light across the sensor as a whole is not affected by increasing exposure, the ratio is greater in the darkest parts of the image and increases further when you increase exposure.
Image post-processing is not free - obviously, in terms of time, but also in terms of information loss. The situation you would not want to use ETTR is any situation you don't need to.