I agree with all of you. I largely prefer 4 players, as I think it's the most balanced. I also think that 3 players is quite an unlucky number, because I have the impression that it happens quite often that one player is cut off the power charge, while the other two happily charge each other. And as the placement of the first mines can follow very individual logics, you cannot really avoid this situation. With four players this happens much less, except if you are playing Taklons, but then that's part of the strategy.
It is certainly true that 3 player tables fill up faster and the game takes less time, especially for turn-based games with players from different time zones. On the other hand, when I started playing on this platform, 4 players was standard in arena, and there was quite an active community, so it was never a problem to find a table quickly. Well possible that these players don't play arena any more, as it is 3 players now for quite a while.
Concerning map setup, I'm more open. I like the variability the random map adds to the game, and on the other hand I don't like it, because it can really create weird setups. This combined with random factions, you are sometimes in situations where you bid more than 50 on a faction, which adds quite some randomness to the results. On the other hand, with the official rules, you end up too often with Itars, Taklons, and Ivits.
Auctions are necessary in any case, however, because you can never guarantee that the 4th player rotates a balanced map.