Instead of reflecting ambient light, why not measure it and then emit the same amount? It should be indistinguishable (as long as you reconstruct the RGB colors properly), so you can use a regular OLED display.
Because a sunny day at the equator is about a kilowatt per square metre. A typical mobile phone display is about 100 cm^2 (0.01 m^2), so you would need to emit 10 watts to match sunlight.
As far as I can tell OLEDs are 20% efficient or less so you would need an input power of 50 W. Even at 60 deg. N where I live we get over 300 W/m^2 in August so would still need about 15 W of input power to the display.
How so? Diffuse and reflected sunlight is still orders of magnitude brighter than you can feasibly generate in a mobile phone.
Perhaps the solution is eye tracking and steerable lasers lighting up the retina directly. That should cut the power requirements by a factor of a few thousand!
It's not about chroma, its' about luma. You would need pretty powerful backlight to match ambient on a sunny day. It will burn battery pretty quickly and require unrealistic cooling.
I like the idea for indoor devices, but the illusion will be immediately broken as soon as you pick up and move around the device unless the ambient light sensor is polling at a high rate