Driver motors, of which the magnet are the key part and the coil being the other, are essential for controlling a driver's motion. The two are the "main dance" pair, with nearly infinite possibilities of what these two can do. These motors can lower distortion or improve efficiency, give more output or reduce non linear behavior. Its the engine of the speaker, so it can be optimized in a million different ways to achieve what you want. Just as there is no single or universal "best engine" for every vehicle or machine, some types of motors work out better for different uses. A diesel with high torque at low RPM vs a gasoline motor with more horsepower at high RPM is a good parallel for the concept. So driver motors vary a lot in their "goal". It is not a simple device.
Field coils were the first drivers, I have a 1939 Stromberg Carlson Radio with a field coil true coax speaker, mounted to a transmission line. It was high end audio in 1937 to 1940 or so. Field coils are not new or a step forward, but a throw back. From an engineering perspective, Neodymium magnets and other super rare earth magnets are what's being used now to design the new generation of driver. Smaller, lighter and more powerful. Its what makes the speaker in your iphone or your computer work.
Brad