First of all, why should DC residents pay no taxes when they still enjoy all the benefits of American citizenship? What you're suggesting is just plain stupid on its face.
Second, it is false to say that they don't pay federal taxes. While many are exempt from certain taxes, the fact remains that taxation is still applicable.
Third, even if we accept your taxation-centric premise, whatever taxes Americans living in certain territories may be alleviated from paying, those exemptions only exist at the will of Congress. Congress can tax those territories at any time, and therefore representation becomes morally necessary even under your faulty paradigm.
Fourth, your premise requires an assumption that the only purpose of the federal government is to levy taxes. What if there were no federal taxes at all? Under President Coolidge's famous premise that "taxes should be lower, and fewer people paying them" only 2% of the population had a federal tax liability. And he paid down a quarter of the public debt.
Finally, all American citizens who live in America have a vested interest in what the federal government does, as the federal government holds jurisdiction over all US territories.
