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.