Is there a specific reason given, why machina based fiends can't be captured for the monster arena?
My best guess is, that they are not made from pyre flies and can't be "magically" transferred to the monster arena. At least, when they are defeated, no pyre flies emerge.
But I wasn't under the impression, that Final Fantasy 10 takes its own rules that seriously, that this would be the only reason.
Btw:
Fallen Monks in Zanarkand can also not be captured.
In Final Fantasy X, there are 5 types of enemies you will fight:
By definition, fiends are considered the spirits of the dead, who were unsent to the farplane. The spirits become consumed by rage or sadness, and use the pyreflies to become the fiends you fight.
Machina and Mech are inorganic enemies. Given that they are not spirits of the undead, they are not driven by pyreflies nor produce them when defeated.
Humanoids are similar. They are organic, but they do not produce pyreflies as do the angry unsent. With your example of Fallen Monks, while yes they are considered unsent spirits in Zanarkand, they have not yet been driven to the point of morphing into fiends. Therefore, those enemies also do not produce pyreflies when defeated.
Aeons are summons. They are produced by the power of the fayth and the summoner. When an aeon is defeated in battle, they aren’t “killed” in the manner fiends are. While yes, they produce pyreflies when defeated, you could say they “retreat and rest” in a sense. Also, aeons are considered boss battles, and bosses can’t be captured either.
With all that said, why do pyreflies even matter for the Monster Arena? Well, the owner of the Monster Arena is actually an unsent by the name of Trema. Trema has the ability to reconstruct pyreflies into fiends. When you defeat a (capturable) fiend, Trema takes those pyreflies and re-purposes them. This is also how he is able to create new types of fiends in the Monster Arena.
Tremas abilities are never explained in detail in Final Fantasy X, which may have brought on the confusion, but is touched on in Final Fantasy X-2 Ultimania Omega.
