FFA can be wholly obnoxious (especially when you factor in severe grudge cycling between teams), but it DOES allow for more strategic gameplay, which is more than just "kill the enemy."

In 1v1 settings, if you're thrashing your opponent, or your opponent is thrashing you, there is essentially no way to recover from it. If you get dogged all match long and there's nothing you can do about it, it becomes really disheartening and really just makes the entire game unfun.

1v1v1 is definitely annoying with sandwiching situations, I agree, but it's also for that reason that it is actually really clever in design.

1v1v1 and sandwiching is meant to keep balance between the three GC. If you're losing in a 1v1 situation, there's no one to save you. And while that might be more "fair" to some, it's definitely not fun if you're on the losing side.

1v1v1 means that team A is kept in check by both team B and C, B is kept in check by A and C, and C is kept in check by A and B. It's a triangle than is supposed to ensure that no one team simply dominates the arena and merrily skips their way to victory.

Now, I know what you're thinking, as it tends to work out in the opposite way, but that's more a reflection on player's abilities rather than the mode itself. Japanese games, for example, are much closer in point values overall than most EU or NA games are, because Japanese players don't tend to fall for grudge cycling as much as NA and EU players do. When this happens, you frequently see games where all teams are at 700+ point values because they're keeping their eyes focused on their goals.

Sure, I definitely agree it's annoying when you get cockblocked fighting one team by another, especially when the battle is getting intense, but it's usually necessary. (Unless you're the Adders on Primal, in which case you just needlessly fuck over whoever you want for god knows what reason).