Charlaquin
Goblin Queen (She/Her/Hers)
Even in this case, the fighter’s player has more decisions to make per-turn; if anything, the two modes of raging and not-raging give the Barbarian player a useful heuristic that can help narrow their options down depending on what mode they’re in.Consider this. You have a champion fighter and berserker barbarian. They are level 3. Everything else is equal.
The champion has action surge, a few uses of second wind, expended crit, a fighting style and mastery. Everything is either passive (always on, factors into every attack) or active (use it this round, goes away next round. No tracking). The choice points are focused on doing your normal routine and occasionally spending a resource to do something different.
The berserker has two modes: raging and not. Access to his features depends on if he is in rage or not. Damage increases, tankiness increases, he can use strength for certain skills, etc. Further, you need to monitor your rage either with attacking or bonus actions. Because your options and abilities change depending on if you are in rage or not, that is more complex than a fighter.
More importantly though, I’ve already conceded that, under the lens you described, one could interpret the Barbarian as more complex than the fighter. However, I would argue that under that lens, the barbarian is closer in complexity to the fighter and the rogue than it is to the cleric and the wizard, and therefore should still be ranked low, rather than average, in complexity. You described it as the low end of average, I’m arguing it should be on the high end of low.