All speakers should use the appropriate magnets (if they use magnets at all), whether Alnico or other material. The woofer and the midrange of my speakers DO use Alnico. The woofer, which is modern could have been made with alternative magnetic material; the very vintage midrange compression driver could not have been made with the current, exotic alloys. I like the sound of my system, although I don't know to what extent the use of Alnico, vis-a-vis the use of other magnetic material, has improved the sound.
It might well be the case that certain current designs would not work well with Alnico. Alnico magnets are relatively weak and may not work well with designs that require a smaller magnet and very high flux density concentrated in a small area. Alnico also demagnetizes more easily, particularly if heated, which would be bad news in designs where high current could cause heating.
There is also the approach of using no permanent magnet in a dynamic driver. I have heard some VERY good fieldcoil drivers. The problem here is that the requirement for a power supply dramatically increases the complexity of a system. Good power supplies are quite hard to find.
It might well be the case that certain current designs would not work well with Alnico. Alnico magnets are relatively weak and may not work well with designs that require a smaller magnet and very high flux density concentrated in a small area. Alnico also demagnetizes more easily, particularly if heated, which would be bad news in designs where high current could cause heating.
There is also the approach of using no permanent magnet in a dynamic driver. I have heard some VERY good fieldcoil drivers. The problem here is that the requirement for a power supply dramatically increases the complexity of a system. Good power supplies are quite hard to find.