Electronic shutter is a step up already. We are now able to take all the pixels at the same time, then tell them to stop collecting (ie, sample each pixel), and measure the information for each color of each pixel serially, capturing data about an image that was taken simultaneously.
This did not used to be the case.
We still have to do some hacks for the HDR scenery, though, however it's not a bad as it used to be, again due to advancements in sensor technology. We now have greater sensor sensitivity and dynamic range, so a photo that used to require a two bracket shot and post processing can now be captured in camera because the sensor can measure both the highs and lows of certain images. In fact, the sensors have become so good that you'll rarely come across a situation that requires more than three bracketed shots to get the entire dynamic range. Older sensors may have required 5 or more bracketed shots.
Your idea, as I understand it, requires continuous measurement on a per pixel basis.
While this is a great idea, implementation remains a problem. Cameras are designed to stream data from the sensor serially. There isn't a line for each pixel to the processor, instead the image sensor has logic that allows the processor to read the value for a pixel, or many pixels, at once but not all at once. It has to iterate through all the pixels, and this takes time.
We can't overcome this because we're not going to be able to have 50 million wires going between the sensor and the processor. We could integrate more of the processing into the sensor, but the sensor is specialized to do one thing, and do it well. Adding digital circuitry would result in more noise, and probably smaller pixels even if 3D ICs were used. Further, the processes used to create a good light sensitive silicon are different than those used to create a good, low power, fast processing digital silicon.
All of these things are impediments, however for some specialized applications they are already being used. Usually in the scientific and industrial area.
But that doesn't mean we're being left out in the cold. As sensors improve, particularly in dynamic range, you'll find that eventually you'll get "HDR" in camera with no brackets - the sensors will simply be sensitive enough to get the full range, and the lenses and camera body will be good enough to prevent bleed, reflection, and other issues that prevent the sensor from achieving its full capability.
So while the idea isn't bad, it's complex, expensive, and we still have room to grow in other improvable areas so that your method may not even become necessary.