I see no reason at all to use large cloak factory, they are not able to do anything against kodachi, this is absolute nonsense

At low density, 4 glaives kill a kodachi, losing 1. In one of your engagements, 4 glaives almost kill two kodachi, even. By the time kodachi era is over, most of your casualties aren't even glaives killed by kodas, it's naked expansions not protected by anything, including glaives. And after that moment, Emissaries kill more glaives than Kodachis ever did.

At higher density, Imp is cheaper than a single Koda, and you have area-cloak on builders.

Bonus points if you place imps under llt's.