The TIFF compression algorithm makes the files smaller
The files are readable by almost any image viewer.
The standard way is intended to be used for light, dark, flat and flat-darks. These files are normally written in large quantities and compression and viewability makes sense. Already some application developers are working on support. See the list at end of the specification in above webpage. For APP the only requirement would be to read TIFF and decode the tag description containing the header information in a string and decode information like date, exposure, gain, sensor temperature.The specification is not set up as a replacement of FITS. It just propose better of use of the existing TIFF file format.