> and if the arrows are too heavy they're not gonna make it, and if you run out of arrows, you're fucked

Enough thrust will make anything fly: if your bow's range is halved by a heavier arrow, maybe switch it out for a crossbow.

It only doesn't make sense if you choose the position that arrows can be switched out but not bows.

or we could just use guns, if we're going to go away that far from the original analogy

Well there's the other possible interpretation where wood refers to the bow instead of the arrows. Thus, the larger bow can impart larger momentum to each arrow