I don’t think perfection (which is a pretty nebulous concept itself) is the only thing that makes the Final Shape, well, Final. The Hive’s Sword Logic hinges on killing everything, and the last one left standing is the strongest, and therefore the only thing worthy to survive:
“This thing we believe — that we’re liberating the universe by devouring it, that we’re cutting out the rot, that we’re on course to join the final shape — I haven’t found a strict, eternal proof. We might yet be wrong.”
If I am defeated, I know that I will fall to something mighty. Something that craves might, something that loves what I love, which is the Deep, a principle and a power, the versatile, protean need to adapt and endure, to reach out and shape the universe entirely for that purpose, to mutate and redesign and test and iterate so that it can prevail, can seize existence and hold it, certain that this is everything, that there is nothing to life except living.
If a civilization cannot defend itself, it must be annihilated. If a King cannot hold his power, he must be betrayed. The worth of a thing can be determined only by one beautiful arbiter — that thing’s ability to exist, to go on existing, to remake existence to suit its survival.
The focus is always on killing others, not living oneself. Even Toland’s comparison centers around one thing “defeating” the other, though he might be talking about Hive Logic specifically and as such just drawing Logic-like parallels. Obviously, the Hive’s brand of Sword Logic is not the only brand, but the Logic does, at some level, require the destruction of the weak in order for the strongest to survive.
Meanwhile, Aksis wants to become a (demi)god, and Fallen religion worships machines as Gods. So, he becomes a machine, because to him machine = god. The Splicers did have the end goal of “evolution,” though this seems to be in terms of ending their reliance on ether and, by extension, the Servitors. There’s rumblings of Vosik wanting to kill stuff:
In due time, Vosik will ascend. All his people will. And worlds will fall.
But the Splicers seem to want ‘perfection’ for its own sake, instead of following the Logic. It depends on how broadly Sword Logic is being defined; if any pecking order is ‘Logical,’ then the Forge- and by extension the Fallen- are practicing the Sword Logic.