This gets to be complicated, of course. In many respects the 'usual suspects' are chosen for good reasons, but I also think that some aspects of design have been settled on because of the woods used.
The most obvious example of the correctness of tradition is the almost universal use of softwood for soundboards. If you measure the properties of a lot of different types of woods it turns out that, for a given Young's modulus along the grain, the softwoods tend to be far less dense. What this means is that a softwood top can be lighter in weight than a hardwood one for the same stiffness, and usually much lighter. Since vibrating strings don't have a lot of power this helps a lot in the volume department.
For the hardwoods normally used in backs and sides the differences are more subtle, but may be significant. In the 'matched pair' experiment I did years ago, using oak and Brazilian rosewood for two classical guitars that were otherwise matched as closely as possible, there were measurable differences in the sound that could be linked to material properties. In particular, the oak I used was denser than the rosewood, and had higher damping. The added density of the oak may have contributed to the fact that it produced less sound for a given input of power, and the higher damping was probably a factor in the reduced treble output of the oak instrument. In both cases the differences were small, but seemed to be noticeable to most players and listeners.
As for designs evolving around the properties of the materials, that's harder to prove, but there's enough data to be suggestive. There's a vector diagram in one of the old Catgut publications showing the velocity of a compression wave in softwood in relation to different grain directions. The velocity is highest along the grain, and lowest across it, but the relationship is not all that simple, and the locus of the end points of the vectors follows a curve that is very much like a corner less fiddle, oo a Baroque guitar. If the top thickness is uniform, the velocity of a bending wave should follow the same sort of curve, and that shape would be the equivalent in wood to a round pan of water: a wave starting from the center would hit the edge at the same time all the way around. The exact shape would vary with the stiffness ratio of the wood, but with careful selection of known species you can get pretty close to the 'correct' ratio most of the time. One has to wonder if the shape of the violin was worked out to maximize the potential of 'normal' spruce and maple; woods that were easy to get in north Italy and south Germany, where the instrument originated. Perhaps, if the first fiddles had been made with oak backs the design would be a little different. Carleen Hutchins did several experiments on wood substitution in violin family instruments, and it seems you can get pretty good results so long as you stick reasonably close to the properties of European maple.
The bottom line, then, is that, while there do seem to be reasons behind the traditions in many cases, some of them may have grown out of the traditions in the first place.
Alan Carruth / Luthier