While I agree to some extent, the problem is that finding common enough materials to use as bowstrings isn’t easy, if we want to keep all this under somewhat realistic parameters. Even using sinews or plant fibres for this purpose looks a bit weird, but it’s accepted for gameplay reasons. What could be use as a replacement for 3ft strings? Rags? Leather strips? Rubber hoses? There’s the problem. Maybe we could craft a toy bow but, with which materials?
Since 0.4 pre and on I’ve noticed that I’m finding more strings as random loot in almost anywhere than before. Maybe that was tweaked, or maybe the RNG is simply being nice for once. All my last characters were able to be equipped with a self-made longbow in very reasonable time spans.
As for options for leveling up archery up to one, you can disarm or trigger crossbow traps. That’s a crossbow and some bolts for free that you can use to level up a bit. This doesn’t solve the problem with the limited, as the amount of bolts is limited (if any) and you’ll lose them after firing soon enough, making this alternative it only viable if you manage to find lots of those kind of traps.
The slingshot idea, that’s something I’d like to see implemented, even without this issue with archery. The problem with these is that they’d need a rubber hose, and we’d need crossbows (again) in order to get one (by disassembling), or try our luck in hardware stores. No bueno.
I think a simple sling would fit better. All needed is a leather strip (or strings… we can’t avoid those, can we?) and some rocks. Maybe a new type of rock, a pebble, could be introduced to be used as ammo, to make it more realistic. It could be crafted by smashing two rocks, or one rock and a hammer (and similar). It would be an extremely crappy weapon in unskilled hands, but experts would be deadly (the quote from Vegetius in the link above is quite enlightening: “Soldiers, notwithstanding their defensive armour, are often more annoyed by the round stones from the sling than by all the arrows of the enemy. Stones kill without mangling the body, and the contusion is mortal without loss of blood.” - hoping for an arrow instead of a pebble says something about the power of a sling in trained hands).