Has there ever been an airliner design involving reducing generator load by installing solar panels?
If no, why not?


While I can't say categorically that it's not happened, I'm pretty sure.

Solar radiance is approx. 1kW/m^2. A 737 has approximately 100m^2 wing area. Solar cells are approximately 20% effective. 

If you covered the entire wings in solar panels, that would work out to 20kW of electrical power at best. At night, it would be close to zero extra power.

Jet fuel contains ~43MJ/kg of energy. 20kW is 20kJ/s. For a 2 hour flight, the total energy produced would be 144MJ, or comparable to energy in 3-4 kilograms of jet fuel. 

Turbines is not 100% efficient, so let's say that with all losses in engine, 25% of the power in the fuel is available as electricity. That means you'd need 12kg of fuel to provide the same amount of electricity as the solar panels.

12kg of fuel. That's probably far less than the solar cells will weigh, probably by a factor of at least ten. In addition, the you don't have to carry around already burnt fuel, unlike solar cells, which you will have to carry around. 

Edit: I found another answer on this site, that claims extra fuel use is on the order of 0.125kg/kWh. I don't know if that's correct or not, nor do I really care. It doesn't change the conclusion, it only makes jet fuel even more favorable.

In short the amount of power provided by solar cells is tiny compared to the energy contained in jet fuel. And that doesn't even touch on the mechanical requirements of a wing...