Many of the Dunmer brought wealth to Windhelm, but was refused to buy proper houses solely due to their race and ancestry, and was herded into what came to be known as the Gray Quater.. I don't know about you, but that would piss me off big time if I was a Dunmer.
As far as I can see Windhelm is not such a big city. And the walled area(thus safe area) is limited and few. It's not like one can expand and build more houses inside the walls.
The Nords have lived there for generations and they all have their own houses, passed down by their ancestors. I don't see any reason they would want to give their houses to others without compensation.
The only vacant house in the city is the one for the player. And even then, the dragonborn(no matter what race he is, Nord or dunmer, same) has to lots of dangerous or difficult tasks and favors for different citizens in the city in order to gain THE RIGHT TO BUY that house. And then, he/she will still have to pay a decent sum of septims for it.
I doubt any of the dark elves there is willing to, or able to do all these things. Not to mention having enough money to buy it.
In medieval times, living in a walled city/castle is a prestige that not many people can enjoy. Most people can only live in unprotected farmlands or huts.
And yet, the Dunmers can live in the safe walls of Windhelm. I think the stormcloaks are already treating the dark elves greatly.