Wait what? Brawny also affects initiative, not just fatigue?
It does. Notably if your archers are wearing Mail hauberks (150 armor, -18? fatigue) – probably gives you around 10-15 initiative back. On the other hand, it hardly gives you a boost if you are wearing named armor (~130-150, -10 fatigue or so). Ideally, I would try to equip my archers with named armor and helmet (~120-180 defense, no sight malus, looks like a direwolf head) so they are somewhat protected against crits and look awesome.
Anyways, while brawny seems nice I think it’s overall a wasted perk point on archers – in my next playthrough I will replace it with recover and see if that works any better.