You've honestly got me thinking here.

Has anyone tried machining an AR-15 lower out of wood yet? I can't think of a single reason that a good chunk of solid oak wouldn't be perfectly viable as an AR lower receiver.

The only problem I can think is that the dimensional stability of the wood might not be good enough to preserve the relationship between the fire control components, resulting in unintentional hammer fall. You might have to stick a small steel plate in there to keep the hammer and trigger pins in proper alignment.

Might also have to beef up the cross section a bit where the stock attaches -- but that's solved easily enough by making the stock integral to the lower receiver.

The upper could be more of an issue -- you'd need some aluminum inserts for the cam pin to ride on to ensure you don't get out of battery fire. Perhaps an aluminum ring for the barrel to screw into to also serve as the rear sight platform. That isn't really a pressure bearing joint though, is it?