The Alexandrians have had the ability to extract souls for four centuries. And keep in mind, they figured this out during a world war. A bunch of people would have been dying on both sides. Some time after that, they figure out the other stuff, regulators, Endless, robo Otis, etc. But the Storm Surge is a war that leaves them the last surviving civilization on their shard. At the very least the last survivors on their continent. So they would have the souls of all those dead in stock. We actually see the stock when Sphene is talking to Zoraal Ja, they have thousands of souls in storage.
I don't understand why you're insisting that the regulators have to come with a soul in them already. You put it on and you buy one. If you put it on and there are no souls in it, then you get all the memory wipes, but you don't get revived after you die, your soul gets stored inside. We actually meet a character with no spare souls, the Arcadion fighter that insults Sphene. He's proof that you can walk around with an empty regulator. I don't understand why you believe otherwise, which is what made me assume you believed the souls were being destroyed.
As for why the system is sustainable, the used souls are stuck in the person who used them until death, which is why regulators are required to keep that person's mind the dominant one. At death the used souls are released back into the aetherial sea, and the unused souls and the wearer's soul are sent to Origenics for processing.
Zoraal Ja not only used up a lot of the supply on himself, his attack on Everkeep meant that a lot of people burned through a lot of souls all at once which would up demand. So yes, due to his actions they are in a state of low supply and high demand, but that doesn't mean it's unsustainable. It means the prices of souls will go up dramatically, which will cause more people to die of accident increasing the supply (and yes, I just realized how dark that is). But it's a system any of them can choose to opt out of whenever they like. No one is forced to wear a regulator.