TIFF is a very versatile container format for various image-streams. It can encode multi-images(likes layers), with different compression (losseless, JPEG etc) and tiled images to read/write efficiently big images e.g. for astronomy, pathology (microscopy). It is the standard for archiving images.
First, this is obviously a problem with the browser ("I can't view a common image standard!"), not the image format (it may have other problems, but "third party software isn't supporting this format" isn't a real problem).
Second, assuming your goal is to study the picture, of course you want to save it to disk.
