Perhaps the souls of Dragonborns are a duality of sorts.....
There is a human soul (which goes to Sovngarde upon your death) fused with a Dragonsould (which remains behind in your body)?
Or its just a gameplay mechanic that they didn't really think through and we should ignore it.
The duality would make sense if we knew any other instance of a mortal body housing 2 souls and one of which is a very powerful one and the other is a black soul....I'd say it was just a reward gameplay mechanism,but then the question would be what held the dragon soul....
My theory:- Jurgen had a lifetime of meditation on the words of power which are the source of a dragons power,this meditation makes his own soul closer and closer to that of dovha and this is what the other practioners of the Way of The Voice try to achive..