I have been wondering about this obstacle regarding the use of EVF for action photography (say sports in general). Don't you think that in the near future, and given the progress in video for some cameras, it will became feasible just to shoot video and extract the important frames from it? Given the not so high requirements from news agencies and print media, I think that it would be a feasible option.
Yes... eventually. To shoot high-quality video and action stills
simultaneously, you'd need to shoot at 1000-2000fps and 32-40MP resolution, with a buffer of at least 40 frames. That's probably a decade away. Yes, 1000fps sounds huge at the moment, but, in terms of data bandwidth, it's only 40 times more than a 25fps 8k video camera (some of which are coming out now), and, using fully electronic shutters, moving parts aren't an issue.
Video requires motion-blurred frames (shot at around 1/40-1/50 for 25fps video) to appear smooth, while action shots need fast shutter speeds to stop action (typically 1/1000 or faster). A video made from still photos will look choppy, while stills taken from a video clip will be blurry. To get around this, you'd need to shoot at the shutter speed needed for stills (1/1000 or so), then add 40 consecutive frames together to create a motion-blurred frame for 25fps video (or 20 frames for 50fps video, and so on). Or just run the video at 1000fps, as the case may be...
Of course, we'll be able to shoot 8k video and action stills
separately well before then - for that, you just need an 8k video camera with a fast AF module that can focus and track while shooting. Basically, a 32-40MP mirrorless camera. Set it to 1/40 or so to shoot video, or 1/1000 or faster when you want to shoot action stills. Not too far off. So, pretty soon, action cameras and video cameras will be the same thing.
Even with simultaneous video/stills capability, you'd still want lagfree EVFs and fast AF while shooting - they're basically separate issues. Although improving pattern-recognition-based AF methods (e.g. face detection, eye detection and now Nikon's 3D tracking) will likely make AF a non-issue by that stage, particularly with a mirrorless sensor that makes use of the full resolution of the sensor for AF, rather than the low-resolution AF sensor currently used on SLRs.