The problems with bows are they they need to be constructed, as do arrows. It may be that such is just ignored but it is also true that we basically have no civilians, so it would be conceivable that building bows would have a manpower cost. This is speculation, of course, but it seems that saying that it is completely free would be premature. There is also the risk that there is an energy cost from carrying the bows. Sure, it is far less than the drone's maximum capacity, but it is still additional mass that needs to be transported. We are aiming for "insignificant" rather than "nonexistent" additional energy expenditure. They will also suffer huge attrition, as they will be dropped prior to combat, and being dropped is not healthy, nor is being trampled.
It is possible that bows would only cost wood, but it is not guaranteed.
Enemy archers require training, we do not have training. Enemy archers can see stupidly far, we don't waste our effort on that garbage. I am not familiar with the rate at which they will thwart conventional defences nor do I know the likelihood of shooting their own people in the back, but I have suspicions that it wouldn't be effective. Perhaps a better place to start would be disposable lances or something... Simpler and more practical given our qualities. And if we want something complicated then we should probably go straight into leverage theory and then into trebuchets...
On the other hand, we are very good at biological manipulation and haven't done much with that. Much of our forces are largely unmodified. I am tempted to do what we are good at, rather than copying the The Loaf at what they are good at.