My short answer is no. It shouldn't.
The long answer? Areial hit it on the head for me.
I always looked at it as though the Dawnguard were safeguarding the coming dawn, making sure that the vampires didn't do anything mess it up. Story points aside, this meant focusing on hunting vampires where they hid as well as watching over settlements throughout the night. Also, they have a few unique light spells that facilitate their hunting vampires and undead.
Note that at a certain point during the DG content vampires randomly attack cities and settlements, so as a member of the Dawnguard your job would be to fight them off and protect the civilians. Especially if you didn't want them killing your favorite vendor who happens to conveniently have a shop right-beside the front gate. >.< Pain in the ass.
Your idea about the Duskguard has some merit to it though, I think. That might have been an interesting play, allowing a small group of vampires to join their ranks, helping them keep the local covens under control while safeguarding the future of the world.
Spoiler What Harkon wanted to do (in theory) was just madness and likely would have been the eventual end of everything, including vampires. Those bloodcursed arrows certainly are a lot of fun though.