peoples excuse why void elves cant be demon hunters is that void light and fel are opposing forces that dont mix with each other.
but thats bullscat, we have had forsaken using the light as holy priests forever, now sure you can say undead are not made using fel or void. but then we get into legion and we got lothraxius or whatever, the light infused demon, that is still classified as a demon mind you.
there was also the naaru that was trying to light infuse illidan despite him being THE demon hunter, and even then the physical traits that the void changed in the velfs should not prevent them from being able to become demon hunters instead. because other mortal races like the orcs that had their bodies changed by the fel can still become corrupted by the void.
thematicly they would fit too with demon hunters being able to have purple tattoos and plenty of purple glowy weapons so why the hell not.
I would play one, they can say those are some of the nightborne who sided with the legion (the felbornes) and they were sent to the illidaris to atone for it.
well as you said Forsaken are not created by fel or void nor are they using fel magics to heals, but in general many things do not make sense , Void elves being alliance only) to begin with , very weak reasons lore wise (utter BS if you ask me) just like nightborn being horde only, IMO those races should be able to choose like the pandas do.
But i digress , TLDR : 1) Blizz do not really want to / 2) many things do not make sense (light forge DK, lol)