gratuitous (and often unconscious) reference to killing birds is offensive. IMHO!)

Belated greetings grump!

I find myself in agreement with Capfka on this one - the phrase is useful, sharp and clear, and to my mind doesn't carry any connotations of real violence, let alone environmental destruction. I suspect the "birds" being referenced were never real, given the practical impossibility of killing two real birds with a stone (with or without a sling). The phrase certainly doesn't have any association with impossible or unlikely outcomes.

This makes me think that the birds are targets in a contest - perhaps standing-up targets for slingshot practice? It would certainly be possible to knock down two stationary inanimate targets with one stone or shot.

grow two trees from one seed
Cute, but lacks the very important senses of speed and finality IMHO. Trees take ages to grow, whereas throwing a stone is pretty much instantaneous. And to "kill" two onerous tasks with a single clever effort is definitely preferable to leaving them niggling away at your peace of mind for years.

Fisk