I struggle with the concept of having one...
Playing 4K on a monitor is pointless. And redirecting 4K from your PC player into a 4K TV uses up too much CPU, while renders a sub-par picture, unless you have a very powerful card with HDMI 2.0.
The only practical ways to play 4K on your large TV is: A) YouTube/NetFlix B) External 4K Player
And I'm not hypothesizing, I'm talking from experience.
I don't think you have any idea what you're talking about, or your setup was screwed up. Sending a 4k picture to a monitor uses the same amount of CPU as sending a 4k signal to a tv. There is literally no difference. Also, the picture shouldn't be worse, unless you have a bad TV or you're like 2 feet away from it. Also also, 4K Blurays output much higher quality video than a 4k YouTube or Netflix video due to less compression being necessary, so online streaming is hardly an alternative to physical media playback. Also also also, graphics cards have nothing to do with 4K media playback in this instance besides sending out the video signal, since playback is handled on the CPU, because Kaby Lake processors are the only things out right now that support the necessary standards. You don't need a powerful GPU, only some with HDMI 2.0.