Soul Crystals are used to speed along the process of learning a new class. We don't just pick up a weapon and master it instantly, we're using the combat memories of the stone's previous owners as our own. (Garlemald's new Weapon program aims to achieve something similar, albeit using much more horrifying methods.)

It's plausible the Echo has something to do with it, but there's no reason anybody with a soul crystal wouldn't be able to pick up on the advanced techniques we use as well. (Except for MCH, which as a completely new discipline has no memories stored in its soul crystal.)