In encode.su I’ve made my point before that the - by now old - jpeg xr would be perfect for this.
It 16bit support is nice, it even supports faux-floating point, which basically means in this case it an encode at 16bit but set a black and white point. So your camera could write an image that could contain ‘overbrights’ so you could reduce highlights afterwards.
16bit tiff, I guess not. But imagine that the jpegs it writes are actually 16bit files and could contain the whole captured range, while still being ‘ready for displaying’ right from the file.
Yes I would use it then. Although my Sony a7m2 is just too old to have the the good in-camera noise reduction and sharpening, so I would still use raw where I would want to extract everything.
But files as big as jpegs, quick to decode even on slower hardware, ready to view, but with enough data to change exposure and white balance afterwards. Sounds awesome to my ears.
And the format is even open and standardized, and uses no different algorithms than basic jpeg (basically increased dct blocks and memory requirements).
Jpeg xl would also work quite nicely, but is new and modern with different algorithms.
Formats like webp and avif and heif can be at most 12bit I believe (correct me if wrong).