I can't feel a tank of gas on my '14 but can on my '98 so I say go for it, no sense hauling around an extra 150+ lbs of weight with gas prices the way they are now.
However, I'd probably keep the 3rd row stored somewhere, in case I ever wanted it back in again, or to sell the vehicle later, can't help resale value to have 3rd row missing and instead a DIY flat panel to level out the cargo area. Keep that in mind too, that after a cross brace, and a panel to cover the hole where the 3rd row was, you are not saving more than maybe 100lbs if that, but the weight will be lower on vehicle center of gravity which is good, and yet the weight is also lower if you just fold down the 3rd row seats. Your call.
I agree with peterk9, if you remove them (especially for *performance* reasons) then you should install a cross-brace, whether it is the Ford part # meant for it, or DIY weld (or bolt) up tubes and plates wouldn't be too hard either if you have fabrication experience.