I have played with removing dirt from the rootball in the past.
There's a couple ways I've done it:
Dry- letting the soil dry out completely and then gently shaking it out of the roots
Wet- putting the whole root ball in a LARGE pan of water and just letting it soak for ~10 minutes, and gently swishing the dirt out. Use water at room temperature!!!!
I have not lost ANY plants to repotting stress using either method.
I did this because I was going from soil to coco and wanted as little nasty old dirt as possible to come along for the ride.
Changing your soil can fix deficiencies if the def is actually a lockout caused by improper pH of the soil the plant had been in, or if it was so rootbound that nutrient uptake was impeded.
But you still have to flush after and then re-start a fert program with an appropriate fertilizer, and that CAN be a fert mixed into the soil, or one that is watered in.