The (in)efficiency issue makes it uneconomic.
Light Emitting Diodes (LEDs) are designed and optimised to convert electricity to light. They are not optimised to convert light to electricity — those would be photodiodes.
A staggering amount of research and engineering has gone into making LEDs consume as little power as possible to produce the maximum amount of light possible — i.e. make it 'energy efficient'. This inherently limits what can be accomplished in reverse. A LED that consumes 'as little power as possible' also produces 'as little power as possible' when forced into generation mode.
The colour of a particular LED also filters out certain wavelengths. Blue LEDs, for example, ignore red and green light so lose another two-thirds of their maximum efficiency. Green LEDs ignore red light so lose another one-third.
Finally, there's the issue of location. You generally don't want to place a screen of any sort into direct sunlight because a) it's hard to see anything when the sun is shining on it, and b) because the UV will degrade the appliance over time. Thus things like televisions will always be placed in the shade — the worst possible place to put something if you want to convert solar energy to electricity.
Combine all this and you end up with a situation where the cost of the additional circuitry required to make LED screens generate electricity (when not in use) is so much more than the value of the electricity that they will generate over their lifetime, that it just doesn't make financial sense. You'd need to keep a TV for hundreds of years for it to generate enough electricity to pay for the extra circuitry.
Consider also this: Solar panels — which are just superbly-optimised, large-area photodiodes — have payback times in the region of 5 years (depending on the cost of local power). Since it's inconceivable that the laws of physics will allow optimised LED generation efficiency to get within an order of magnitude to that of optimised photodiodes, that means the best case scenario is that you would need to keep your TV for 50 years before the added investment had even the slightest chance of paying for itself.
So, is it possible? Yes. Does it make economic sense? No.