Here are some of the reasons while still picture quality is considerably higher than video:

• Resolution Even 4K video is only about 8MP. Standard HD (1920x1080) is only about 2MP. Most current DSLRs are upwards of 20MP. All of that resolution comes at a price, though: larger data rates per frame. And it's not just the total number of pixels per frames, it's also how they are compressed and saved.
• Compression Video tends to be much more compressed than still images. This is because some of the artifacts caused by heavier compression average out from frame to frame. That's a lot less of a problem at 24fps than it is for a single still image, so video codecs can get away with higher compression.
• Codecs Still images are recorded with all the information needed to display an image in each frame. Most video codecs record an initial frame and then record only the differences between each frame and the frame immediately preceding it in each successive frame. Again, the lower image quality of each individual frame is not noticeable at 24fps. The resulting savings in terms of data rate can be quite substantial.

It works out that about 20-30 HD video frames are roughly the same size as a single 20MP RAW file. To put it another way, you can store an entire second's worth of HD video in the same space as ONE 20MP RAW file. And that is only 1920x1080. 4K would require the same as one 80MP still image (It's both twice as wide and twice as tall in terms of resolution, so there are four times as many total pixels). Even at JPEG compression that's still about a 20:1 ratio.

So to get a camera to record video at still image quality, the data rate would need to be increased by a factor of about 24X! To record even one minute of video at 20MP and 24fps using still image compression and codecs would require the same amount of data as 1,440 frames of a 20MP image! Current memory card technology isn't even close to that kind of throughput.

Then you would need to have a memory device capable of storing all of that data. You could fill up a 128GB memory card in only a few seconds of recording. You've also got to consider the power needed to process that kind of data rate in a DSLR sized package. The best cameras from Nikon and Canon can go about 2,000 frames on a single battery. The same amount of data required for 2,000 raw files will get you about a minute and one half of 20MP /24fps video.