Its a philosophy, and has persisted as the dominant philosophy on the Thu'um for longer than its use as a weapon.
Interestingly enough I think that trend might be reversing as of 4E 201. With Ulfric shouting down Torygg during a duel “in the old way”, the Ebony Warrior using Thu’um, and potentially the LDB taking a side in the ongoing civil war.
Now I sort of wonder if this is an intentional narrative within Skyrim. IE is the return of the Dragons and the Stormcloak rebellion slowly spurring some sort of revival of Ancient Nord custom (pre Jurgen)? Arguably the use of obscure and ancient songs by the bards (Tale of the Tongues) which feature the Thu’um in that light could be seen as part of this.