Unreal does support DDS files, I’ve imported them plenty of times.
As for TIF files. TIF is easily my favorite format to work with because it’s little or no compression depending on if you use LZW compression or not. However, because TIF files don’t compress information they take up a massive amount of space in comparison to formats like DDS and Targa. A 4k 16-bit TIF image can often take up more than 100MB of HDD space, while the same image saved as an 8-bit Targa file will come in at a drastically lower space requirement, I’d like to say it’s usually around 40MB,but I’m not sure off the top of my head. Even with the extra compression that UE4 does to textures on import, it would still take more time for UE4 to compress the data from a much larger file than it would be to simply resave that file as a Targa or PNG.