I’ve seen some where the entire image dynamic range is in the range of 0.0 to 1.0 and that clearly doesn’t work very well if you just truncate.
That is relatively sane compared with some formats I have seen. SWarp, in particular, can generate values which are negative and in a range which bears little resemblance to that of 16-bit signed integers. The result is fully compliant with the FITS standard and, for example, ds9 has no trouble dealing with such images.
That’s why I had to write my own conversion routine.