Yeah I never understood why the inquisitor gets a free handout instead of finding theirs. Going a step further, why don't the Sith toons get to build their lightsabers to conclude their training on Korriban like the Jedi do on Tython? Is there some lore element I'm missing?
As far as Kotor goes apprentices were sent into the tombs as a form of their final trial. There they would find the lightsaber that would be theirs if they could have it. A sith apprentices lightsaber represents the fact that he had the power and cunning to overcome dangers of the tombs to retrieve their lightsaber.
As for the inquisitor, you could argue that Zash felt the inquisitor met all those things and thus deserved his lightsaber