He can "book" a free FC seat on both United and American. He does both. Why wouldn't he?
I use United, American, and Southwest for my commutes. I can fly all three for free, I just can't "book" a seat like he can. I only get on the flight if a seat is left over. My last commute ended up being SWA both ways, which is unusual, as UA and AA have more flights. It just worked out best this time so I took them.
I agree that it's a good idea for airline managers and executives to fly on the competition with some regularity. Gets them out of their bubble. They get to see what their airline is doing better, and what the competition does better.