Very probably because they don't have the resources (people, space to sort, places to dispose of it) to deal with the unusable stuff they're likely to get if they don't specify "new new". (I volunteer in a charity shop and some of the junk that's donated to us is unbelievable.)

It may also be a question of wanting to make those women feel valued and to boost their self esteem — that they're deserving of new stuff, not someone else's cast offs (which I know could be beautiful and in beautiful condition, but it's still someone's "discards".)

And going back to your "undonatables", Spiffikins, check if your usual donation place can take bags of stuff for "rag" (that's the stuff they reject and send to recycling). If they do, they may be willing to take those two bags if they're clearly marked as "rag" or whatever term they use, rather than you putting them in the trash.

Also, well done on finding so much stuff to unclutter!