Because when you mix 2 things at temperature T, it doesn't make a thing at temperature 2T. Don't mistake temperature for energy.
It depends on what kind of "mixing" you allow. You could have an array of 1000K lamps shining on solar panels, then combine the solar panel outputs to drive a small 2000K lamp. Certainly there would be a lot of energy loss in this system, but the temperature would increase to 2T.
So without specifying the constraints on the collection system, you can't say that a 2T increase isn't possible. The solar cell method has only passive components, so passive alone is not sufficient to forbid a 2T increase.