Summary:
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- jpeg is best format for lossy compression of normal photographic images.
- tiff is a good format for lossless compression of photos (or anything else), if:
- it's supported, and
- filesize is a don't care, or you can use non-standard compression (tiff extensions).
- png is a good format for lossless compression of non-normal photographic images or screenshots etc, or lossless compression of photos, if:
- tiff not supported, or
- filesize would be less than tiff, and that would be a compelling factor.
Lossless display on the web is one of the most frequent cases calling for png.
(this is not intended to be an exhaustive list, but in the context of Lightroom - still images, no transparency, etc..).
To be clear: nobody is suggesting png over jpeg when lossy compression is adequate.
PS - removing icc-profile to reduce jpeg filesize is NOT a good idea, unless you KNOW the device being used to interpret it will do it correctly without the profile.
Bottom line: most of the time jpeg or tiff will do nicely when exporting lossy or lossless images (respectively) from Lightroom, but if Lightroom supported exporting in png format too, it would also cover the cases when png is desirable, or necessary.
I guess we've beat this subject to death now - sorry..
Rob