I'm not 'bad faith arguing', and in jumping in with that right away you're clearly showing that you're not really coming into this in good faith yourself; you just want to come in with a cheap gotcha. But I can tell you why this is, at best, a bad idea:
'Consumption of ambient aether' has been an actual raised crisis point for primals three different times: Ramuh, Alexander, and Eureka. On top of that, overconsumption of the land's aether was the cause of the Sixth Umbral Calamity, the flood that ended the War of the Magi. Draining the world dry like that causes a complete wasteland like we saw from The Burn, itself a non-primal instance of overconsumption of ambient aether, from when the Allagans launched Azys Lla. So far from being a completley harmless thing you could do, a primal is capable of rendering the land a barren wasteland just by being summoned. We even have some general indications of how much aether that takes; the Students of Baldesion theorized that Eureka could've drained the entire planet by just recreating the Mothercrystal--and as deeply-connected Sharlayans we can reason that they probably had accurate measurements of how big the Mothercrystal is. But perhaps even more damning: Alexander was capable of being a Calamity-level threat just by consuming the aether needed to walk. So no, I don't think Zodiark could be made by doing that without causing just irreversible harm.
But your argument is that if we just do that slowly it'll be fine. That they just siphon off tiny little bits of aether until they have all they need. Honestly, in this context I'm not sure that works; first of all it seems to presume that there's a constant supply of aether coming to the star somehow, maybe like how Earth gets energy from the sun, but I'm not entirely confident that's how it works. In fact, my counterargument would be The Burn: if there were a constant supply of aether enough to replace a Zodiark's worth of ambient aether, I think the Burn would show signs of recovery, and it doesn't.
But even putting aside the plausibility of the plan itself, there's another problem: you seem to be naturally assuming that they have a lot of time. And honestly, I don't think they have that much: the only indications of time having passed is that Fandaniel was now in the seat, and that later on Venat had recruited twelve friends. There's no indication of aging, natural death, or of changing life circumstances; the descriptions of the Twelve's predecessors sounded like people who knew each other as a snapshot, not over a long period or perhaps even that well. Menphina was young, you'd expect an over-time description would mention her growth. I've always gotten the idea that they had about a year or so. Not nearly enough time for them to have initiated and compelted a public works project so slow that it needs to be outpaced by natural regrowth.
EDIT: Had another part to this, but I was thrown off by ambiguous terms; Iscah's got the better explanation on this one.