JPEG also supports lossless compression.
Technically, the spec does require it, but given that we’re in a thread about ecosystem support for a file format that’s approaching its 15th birthday, it’s worth considering how many image viewers will actually be able to work without the DCT step that is the essence of what typical JPEG does.
I don’t have a Windows machine handy to test, but it’s entirely possible that maybe lossless JPEG won’t display in its default viewer.
Generally, those who need to ask how to install a drill bit into a drill are not typically the people who should turn around and immediately proceed to drilling holes into important things.