When 4k videos come out people will probably want to shift back to hard drives for the sheer size compared to SSDs when hard drives are like 6TB+.
I'm not so sure about this. Let's rule out super noisy video. It's hard on the compressor engine and it's hard to tell where to top out the bitrate.
Let's also assume we're talking about good quality h264 two pass compression. And your average movie. Not a short that involves pure motion, water waves, etc...
I've found that SD material can be compressed very well with a bit rate of 2mpbs.
Moving to 1080p, which is roughly four times the pixels, compresses visually in my opinion just as well with a bitrate of 4-5mpbs. Or just over double. Not quadruple as the increase in pixels would suggest. Based on that I think 4k will compress just fine at 8mpbs. Also I expect any new 4k video will be shot digitally and be very clean. And anything worth moving to 4k will also probably have been cleaned up pretty well.
I think it has to do with the amount of edges in a frame of video, which is basically the same at various resolutions. That's where a lot of the extra bandwidth goes at higher resolutions. The non-detailed areas, sky, streets, blurred out background, are "averaged out" by the DCT matrix in the compressor and require very little data to reproduce. If the detail isn't there to be seen my human eyes then the compresses doesn't allocate much data to it.