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I always thought it is better to underexpose vs overexpose, if you don't correctly expose.
gawd i'm dum.
:/
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That may be true for your brand of camera. Most, however, have a LOT of flexibility in recovering highlights. Several stops above what the camera says is over exposed in any case.
Underexposing will certainly preserve those highlights as well, but you will likely add a considerable amount of noise bringing the rest of the image up to proper exposure.
ETTR is not a hard and fast rule, there are situations where it does not work. The big one is super high contrast situations without the ability to use fill flash or something to help balance stuff out.
Nikon cameras in particular tend to be what they call ISO invariant so an image at ISO100 pushed up to ISO6400 equivalent will contain about the same amount of noise as one captured at ISO6400 in camera. Not all sensors can do this. Some are cleaner if done in camera, others are cleaner if done in post.
ETTR at its most basic is trying to improve the signal to noise ratio. Images shot using ETTR require a bit more processing than those done with normal exposure, but they tend to contain a lot more data. Better highlight data, better shadow data, a lot more range than is typically expected.
Someone that is good at ETTR and processing them can damn near get HDR composite level of details and range out of a single raw file without all the weird artifacts that come along with HDR.
ETTR also helps to get less noise than expected for a given ISO value. Part of the reason my D500 shots were virtually indistinguishable from my D750 shots (thus leading to the D750 being sold) was ETTR essentially getting rid of the crop sensor ISO penalty.