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I think so. So, I was trying some video on youtube that is 4k, it lags like cazy, on both of my PC. They're very fast, one with an i5, anohter with an i7.
None of the browsers seem to use the GPU to render, but still, state of the art CPU are not even fast enough to render 4k video. It shows how much extra power you would need to go from 1080p to 4k.
4k would require rendering 4 times as many pixels, to get the same speed as 1080p, you would need 4 times as fast a GPU, 4 times as fast RAM to load 4 times as much texture data, 4 times as much bandwidth.
If your PC now does 120FPS @ 1080P...it will do 30FPS @ 4k..at best, probably less because you will not even have the bandwidth for it....no sane person is going to accept such a hit in framerate.
It's neeever gonna happen. At least not in the first couple of years. No one is going to accept 4 times less framerate for a few more pixels.