The difference here is that the Black Tower is much more geared towards a frantic arms race to fight in the Last Battle. They, quite simply, have chosen what they see as the most... well, "expedient" method. As horribly cynical as that might sound.
Which is perhaps a sentence that can help new readers of the series to appreciate just how messed up Rand's situation is, and the exceptionality of the Black Tower.
Eh, honestly I think this is more of an issue of economy more than anything. The White Tower doesn't have the resources to prioritize the humanitarian concerns of Gentled men above stuff like international politics and so forth.
Another aspect might very well be that the male madness and...