As the title says, it would make sense if it was rechargeable for 2 main reasons;

1. Classically in other games a staff of the archmage has a few spells it can cast per day like fireball and lightning.
2. As it is, it's a barely useful weapon. Yeah, more Ma is nice, but just not worth dropping a shield and higher damage weapon.

So my proposal is to use the new rechargeable staff function to make it shoot (improved) fireballs.