Note that HDMI 1.4a/b only supports 4K resolution at 24/25/30 frames per second. This is fine for watching movies, but not for gaming. 4K resolution at 60 frames per second requires the yet to be released HDMI 2.0. Or you could just use a DisplayPort 1.2 connection.
So? That's hardware, not software. The software should support any resolution setting under the sun. Its the drivers/hardware which need to be concerned about bandwidth, connectors, and whatnot.
And how exactly do you expect the software to support something the hardware doesn't support? If every software group thought that way the computer industry would be destroyed. It doesn't matter what the software is capable of if the hardware can't do it, so it's better to not let the drivers say "hey look, I can do 4k screens!" and someone attaches one only to find out it doesn't work due to a hardware limitation. This isn't the same thing as having a CPU too slow to play a game, because the game will still run. If you buy a 4K screen because your drivers SAY they can support it, you're going to be pretty unhappy to find out the screen won't even leave standby.
Setting screen resolutions is a lot more complicated than most people are aware of - there's a lot more than width, height, color depth, and refresh rate. It isn't as simple as just flicking a switch and suddenly getting 4K resolutions.