Do I need stills if I'm shooting video

Well, look at this way, a screen grab from video is very low resolution compared to a true photographic still. That's true if you are using a compact camera, and even more so if you are using higher-end cameras.

Video resolution is a very thin 1 megapixel, even at high definition (HD).

Compare that to the 10+ megapixels from compacts and the 20+ megapixels from DSLR's and you see there is no contest.

Could this change with cameras like the Red?

OK, Red cameras are much higher resolution video cameras, principally aimed at the cinema market where much higher resolutions that HD video are required. They can also be used as still cameras.

I can see that from a technological viewpoint it will be possible to capture video at the full resolution of your cameras sensor sometime in the not too distant future. So you could capture some humongous 20 megapixel video.

But, it seems to me that video and stills are trying to capture two entirely different things, video is trying to capture a period of time, stills are trying to capture the moment. You are looking for something quite different.