We could have a nicely ETTR image in Lightroom, beautifully exposed so that the histogram sits snugly between 0 and 255 (or nearly) and everything is fine. If we then bring it into Photoshop and convert it to, say, Beta RGB, we will most likely be clipping colors at the highlight end (easy to see by doing a soft-proof first). If we drop the image brightness before doing the conversion then the colors will remain in gamut. However doing that damages the image ... and to get the colors back in gamut needs a severe brightness adjustment. Not quite so bad in 16-bit, but very bad in 8-bit.
No, do not use brightness to solve OOG colors issues.
ETTR has a meaning only for a scene referred image, once you are ready to go to photoshop it should not play any role.
Do not rely on the histogram alone. The attached files (extending the point made by Jim Kasson) show the case of two different images whose RGB histogram span from 0 to 255 in all channels. The first is three gradients that go from neutral gray (127,127,127) to the extreme of every channel (255,0,0);(0,255,0) and (0,0,255).
The second image is just a gradient from black to white and again the histogram span from 0 to 255 in all channels. The missing piece of information in histograms is that it does not show if those values occur simultaneously as in the black to white gradient or at different locations.
The third image shows a gamut warning converting the first image from ProphotoRGB to sRGB (it is in softproof mode, so it shill shows the histogram in Prophoto RGB). Do you think that adjusting image brightness will be of any value? Not at all, using exposure or brightness to solve a blown out channels is the wrong approach. It only works if the issue is luminosity and not saturation (look at the luminosity histogram, there is nothing to adjust with brightness)
The last image shows how the histogram looks if we converted to sRGB without doing any other adjustments. Huge spikes in each channels (all channels blown out) and yet the luminosity well below the extremes.
If your issues are with OOG colors, then you have to work with saturation, vibrance, mask, etc. but not with the brightness or exposure
The same can happen at the dark end.
So, this would indicate to me that if we intend our destination to be in a smaller space than ProPhoto (which we almost inevitably do), then we should open the image from Lightroom to Photoshop in a working space that is not too much bigger than the destination (which currently means opening into ProPhoto and then converting to the smaller working space unless the smaller space is sRGB or Adobe RGB), and we should make sure that the image exposure is adjusted to that space before opening it into Photoshop.
The fact that a color space is smaller in volume than another does not mean that all the colors in the smaller space are contained in the bigger space. Color spaces do not behave like a matryoshka where the bigger contains the smaller. This is especially true with output (printer/paper) profiles. Do you know that AdobeRGB has colors outside of ProPhoto RGB? If you perform an absolute colorimetric conversion between them this actually happens, if you perform a relative colorimetric conversion then AdobeRGB is fully contained in Prophoto. What plays a role here is the white point (D50 vs D65)
This is also a good reason to use a raw Smart Object in Photoshop. Open into Photoshop and convert to Beta RGB (no need to be careful in Lightroom). Go into the Smart Object and soft-proof to the print destination and adjust the exposure, contrast etc (and saturation of individual colors if necessary) to bring the image (more or less) into gamut for the destination. Then convert to the destination and print. (I'm leaving out editing steps in Photoshop ... and of course these could result in destination OOG colors: these can be fixed by going back into the Smart Object, or from within Photoshop itself, or by letting the CMM do its job).
Robert
Using a smart object is a good recommendation, convert to Beta RGB might work for some images, not for others.