Speaker magnets

I believe the stronger the magnet the more efficient the speaker.
Also of interest is a technology called "Field Coil" speakers.
This technology uses the current from your wall outlet to create the magnetic field eliminating the magnet.
From dagogo.com: 
"A field coil speaker uses two coils; the voice coil and a field coil. Instead of a magnet, DC is applied to the field coil creating a magnetic field. This takes the place of the permanent magnet in creating the fixed magnetic field."

I have a pair of 1980s Gale GS302 speakers that have damaged woofers, the tweeters are okay. They are a two way system + a passive radiator. I have stripped them out and they are made of nice thick material with plenty of bracing and doubling up inside.  I may go with them for a first project, I have had thoughts about them before. I had a plan to fit a midrange where the passive radiator was, but inside its own isolated stuffed tube, somewhat like the B&O S45 II. Then make a cut out in the rear and fit a modern passive radiator at the back. Use the 8" Kevlars and a pair of 6.5" for the mid range, then connect them up with a decent quality crossover unit. They would look a little odd as the woofer is mounted in the centre. That means it would go tweeter, woofer, mid range from the top down. I have no idea if swapping the normal woofer mid range layout would have a detrimental effect.

@dweller

To my mind that would just introduce the possibility for another source of noise?

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

Check out the magnets on ATC speakers.  The you tube video of the factory is informative as well.

Magnet material plays a role as well.