There have been voice coils without supporting bobbins. L.G. Bostwick's 596A tweeter used an unsupported edgewound aluminum coil which was glued directly to the aluminum diaphragm. Smith and Selsted used (I think) a two layer round wire aluminum voice coil similarly glued to an aluminum diaphragm. In both these instances the goal was to minimize mass to extend the high frequency response.

The Western Electric 555W compression driver used an edgewound aluminum voice coil, and was in large scale production by 1926 or 1927. I believe this was the first use of a ribbon wire voice coil in a loudspeaker. The U.S. Patents #1,707,544 (A.L. Thuras) and 1,707,545 (E.C. Wente) describe the driver in detail. The particulars of the voice coil design and construction are discussed in depth in Mr. Thuras' patent.