Why do you think the DO gave Balthamel a female body?

Demandred considers at the Tea Party in WH that "bodies for transmigration supposedly were chosen by what was available, yet Osan'gar and Aran'gar were proof of the Great Lord's cruel sense of humor."

I actually don't think that the DO gave these bodies because he thought it especially funny, but simply because it would be a strategic advantage to have a male channeler in a female body, if you want to infiltrate a society with female channelers. And also Osan'gar's rather nondescript body makes sense, if he should join Rand. I wonder if Demandred didn't already know at this point where Aran'gar stayed, otherwise he had to see the advantage of a female body (but Mesaana likely told Demandred).

Apparently Demandred doesn't know that much about transmigration anyway, though, as the word "supposedly" indicates (this might explain, why he doesn't realize that a too less capable body can reduce the OP strength, like apparently in Cyndane's case).

Does everybody agree that the body comes from someone in the Borderlands, like SH tells? In this case, it makes sense that Cyndane's comes from the Borderlands as well (BS implied the same in a Q&A).