Re: why not wood?
There's really only one - moisture. A homogeneous wood stock that has not been properly sealed against moisture will expand, contract and possibly warp as the ambient moisture content of the surrounding environment changes. This can lead to bedding changes, pressure points on the barrel from the forearm shifting, compression of the wood at the action screws, and a number of other horrific things that can happen to wood when it is exposed to the elements.
Laminates, by virtue of the wood being impregnated with the resins used to glue the layers together, are not (as) susceptible to moisture as plain wood. Synthetics are just not susceptible to moisture at all.
It is certainly feasible that a nice wood stock that has been properly bedded so that the bedding compound completely seals the bedding area, and then filled and/or sealed to make it as water resistant as possible, would shoot and continue to shoot as well as a synthetic stock, as long as it is maintained.
As hideous as the old gloss epoxy-based Remington BDL finishes are/were, that stuff sheds water like a duck's back.
One of my "someday" projects is to get a nice claro or black walnut blank and have Joel Russo carve an A5 out of it. I think a classic piece of wood would be perfect for a retro-type rifle, probably chambered in .30-06.
The short answer to your question though is that wood can be used, but is much more maintenance-intensive than a laminate or synthetic.