Only weak players will suggest double elimination. Because it gives them at least some chance of winning. But try to beat 9 opponents who have passed all the qualifying rounds and score the most points – you'll immediately feel the difference. Considering that the final stage of the Factions Battle selects players who are tournament winners.
There's always a chance to win, ask Aiwe :) The round-robin system creates a lot of problems, especially in the later stages – loss of interest, a lot of meaningless games, the possibility of match-fixing – there are more drawbacks than advantages. The game should be played in a single-elimination format; otherwise, you get this kind of mess, and you can't avoid arguments.