Dynamic range is probably a more critical improvement to be made but the sensor technology itself seems to be the limiting factor here.
I was pondering this recently and wonder if it's the sensor or limitations of ADC technology? It's pretty easy to get a 24-bit delta-sigma converter, but they normally take in the order of thousands of samples per second at best. For say 20MP at 8fps you'd need a 160MHz minimum sample rate. Looking at a few manufacturers while some have products that can do that sample rate at 16 bit resolution the ones I took a quick look at only had 20MHz odd analog bandwidth which I imagine would be "OK" but presumably would give some softness around sharp contrasty edges.
I work with embedded electronics but not imaging, so my comments are far from expert, but I thought I'd throw it out there that the current 14-bit sampling is probably pushing the limits of affordable and practical analog converter technology. To "fix" the problem the usual way would be to use an array of ADC converters, but they aren't real cheap at the high-end and draw quite a bit of current. I think it will change over time as they become cheaper and draw less power all the time. At the moment using an array of converters (or more if they already use that idea) probably wouldn't be off the cards for a 1 series camera from a cost / size point of view, but I imagine it might slash battery life by an amount a lot of people wouldn't care for.