You have a preconceived notion that the material of a driver has to naturally vibrate at the same frequency as the material of the instrument it is trying to reproduce---in other words, have the same resonance characteristics. That is such an incorrect notion, one doesn’t know where to begin to explain why. Where on Earth did you get that idea?!
To reproduce a single frequency (to make it simple), the driver moves forward and backward a certain number of times per second. What the driver is made of is (sorry) immaterial. It is the movement of the driver that creates sound, whether the driver is made of paper, plastic, metal, or wood.
The funny thing is, different materials DO have different sounds, to a degree. But that is a separate thing from what you are asking.