Again, this is a connector from your mobile device to a display. Nobody has ever done any lossy compression on that pathway; both because you can drive simple circuits at frequencies high enough to have plenty of bandwidth and because it would actively destroy information (hence lossy). This is such a big problem because the video you are playing has already been lossy compressed (H.265) and it will most certainly not get better by a second pass that only has the raw pixel data available.

I could imagine people want to play 4k movies from their mobile device on their TV, but you wouldn't install a 4k screen as the display on the mobile device.

Edit: Yes, computer is inaccurate. I wanted to get the idea across that we are talking about connectors (DVI, HDMI) that you would normally use to hook up a computer or laptop to a TV or LCD. They have only recently appeared on mobile devices, but serve the same purpose here: video (and audio, for HDMI) out.