(I think DC statehood does sound like a complicated mess, and the best solution -- if politically feasible -- would be to shrink it. You'd have the populous city of Washington, MD, and a tiny federal District of Columbia, coexisting like Rome and the Vatican. The problem is that Maryland doesn't want it.)
Originally DC residents would vote in Virginia or Maryland Congressional elections depending on where the territory was taken from (note: all DC land that came from VA has been returned to VA).
I think the idea originally is few would live in DC; it was tiny for a long, long time. But that's no longer true, hence why we gave DC the right to vote for President. Congress would be trickier given the balance of power, but none of the original motivating factors apply.