I'll agree that this is possible, but, in forty three years of attending pro tournaments, I don't remember anyone choosing to lose for this reason, and I have countless friends among the pro players.
As you correctly note, the limitation of this method is that a one loss player may be eliminated while another one-loss player wins, but the event is best viewed as a qualifier up to the last sixteen.
At the Olympics, the guy who qualifies third in his semifinal heat for the 100-meter run might edge out the guy who won that same heat later on for the gold. Even though each of them beat the other, all that matters is who won in the final stage. A case can be made that the guy who won his heat and came second in the next stage outperformed the guy who came third in his heat and then won gold, but it doesn't matter. Qualifying is qualifying, and once you have qualified, you on exactly even footing with everyone else who qualified, regardless of how you got there.
The same principle is in play here.