There two main points of contention I'd have, because, lore wise they're a pretty big deal...
First, the Burning Legion threat has been dealt with, the driving force behind the creation and training of Demon Hunters is no longer there so what motivations are there to become a Demon Hunter? I'd be "satisfied" with them going....because I want to...but honestly that really doesn't make sense and is really really weak. Unlike new Death Knights, where the current Lich King is the one who raised them, that makes absolute sense.
The book "Illidan" goes pretty in depth on what becoming a demon hunter entails, and one of the cinematics touches on it, as does the current starting zone. One of the main points is that the candidate literally consumes a demon to become part demon and obtain demonic powers so that those powers can be turned against the burning legion. Constantly fighting the urges to give into the demon's will, or be fully consumed by the power, which brings me to my second point, specifically for Void Elves...
The Void Elves are already constantly dealing with the whispers and torment of the old gods, becoming a demon hunter would put even MORE whispers and urges inside them to contend with. I doubt a Void Elf would be able to handle becoming a Demon Hunter without becoming a murdering, rambling, literally insane, psychopath.