Of course you can... thing is, that stay has it's sag modulated by the backstay tension, so the intrinsic lack of stretch in the rod is usually not worth the extra cost.
Shrouds, however can benefit from rod rigging. Like everything else, it gets back to the cost/benefit ratio.
My class of boat has been rigged with rod and wire, and unless an owner is competing at a pretty high level it probably makes a rather small difference in the real world.